Combine like terms calculator is a free online calculator to combine like terms in equations helps you to simplify equations by combining like terms. However, terms that include the same variables raised to the same power are referred to as like terms. Meanwhile, the only difference is in the numerical coefficients. However, we can only combine like terms in an expression.

Meanwhile, to make algebraic formulas easier to work with, we combine like terms to shorten and simplify them. Moreover, we raise the same variable to the same power in similar terminology. 5x + 10x is an algebraic expression with like terms, for example. We can add similar terms to this algebraic statement to simplify it. As a result, the supplied expression has been simplified 15 times. Similarly, on comparable terms, we can execute any arithmetic operations. When it comes to solving polynomial equation issues, our Combine like terms calculator tool is highly useful because it makes the computations process quick and simple.

Combine Like Terms Calculator with Steps

However, it’s quite easy to use a Combine like terms calculator to combine similar phrases. All you have to do now is follow the prompts.

1st step:

First, paste the entire equation into the first input box, which is located across from the “Enter Terms” area.

2nd step:

Then select “Combine Like Terms” from the drop-down menu of the Combine like terms calculator.

3rd step:

Finally, when you select “Combine Like Terms”, the calculator will bring up a new window with all of the related terms combined.

Calculator Use

Use order of operations such as PEMDAS, BEDMAS, BODMAS, GEMDAS, and MDAS to solve arithmetic problems. (Warning: PEMDAS). This Combining like terms calculator solves math equations involving positive and negative integers, as well as exponential numbers, by adding, subtracting, multiplying, and dividing them. While adding equations, you can also use parentheses and numbers with roots.

Use the following math symbols in our Combine like terms calculator:

+ means Addition
– means Subtraction
×, which means Multiplication
/ means Division
^ means Exponents

(2^5 is 2 raised to the power of 5)

r means Roots (2r3 is the 3rd root of 2)

() [] {} means Brackets or Grouping

You might try copying and pasting equations. However, our Combine like terms calculator will try to convert them to / and * if they use ÷ for division and × for multiplication, but you may need to retype copied and pasted symbols or even entire equations in some circumstances.

Combine Like Terms Calculator Fractions

However, if your equation has fractional exponents or roots, the fractions must be enclosed in parenthesis to use our Combine like terms calculator. Consider the following scenario:

5r(1/4) is the 1/4 root of 5, which is the same as 5 raised to the 4th power. Similarly, 5(2/3) is 5 raised to the 2/3 power.

Enter 1/2 as (1/2) if you want an entry like 1/2 to be regarded as a fraction. In equation 4 divided by 12, for example, you must enter 4/(1/2). The division 1/2 Equals 0 then. The number 5 is done first, while the number 4/0.5 = 8 is performed last. If you type it wrongly as 4/1/2, it will be solved as 4/1 = 4 first, then 4/2 = 2. Answer 2 is incorrect. The correct answer was 8.

Like Terms Definition

A “term” is a mathematical component in an equation that can be either a constant (just a number) or a variable (something that changes) (a combination of numbers and letters that possibly have exponents). However, the coefficient is the number portion of a variable. The following are some examples of terms:

3 is an example of constant

2x is an example of variable

5y^2 is an example of variable

3x2y^3 is also an example of variable

However, words with the same variables and exponents are referred to as “like terms.” They don’t need to have the same coefficients.

Like terms	Unlike Terms
2x, -7x	2x, -7y
-8x², 3x²	8x², 3x
12xy, -4xy	12xy, -6xz
5x²y, -3x²y	5x²y, 3xy²
x, 4x	x, 4

Combining Like Terms Definition Math

When you first started learning to add, you could have come across issues like this: ‘Ram has three apples, and Raj has two apples.’ How many apples do they have together?’

Meanwhile, ‘Ram has three apples and four oranges,’ the challenges might have looked like this as they became more intricate. Raj has two apples and six oranges in his possession. How many apples and oranges do Ram and Raj have if they put all their fruit in one basket?’

You can’t just mix objects at random without regard for their type when solving this challenge. You can’t add them all up and then mix and match the words like they have 15 ‘apples’ or ‘sponges.’ To solve the problem correctly, you must add the apples (five total) and the oranges (ten total) separately.

However, the problem with combining like phrases is similar to the problem with apples and oranges. We can only add terms that are the same (or subtracted). You also don’t mix variables because they won’t change.

For example:

4x + 3x

=(4+3)x

=7x

Using more than two terms as an example:

2r + 1 + (-4r) + 7

=2r – 4r + 1 + 7

=(2-4)r + 1 + 7

=-2r + 8

Using more than one variable as an example:

3x + 2y + 4x + 7 – y

=3x + 4x + 2y – y + 7

=(3 + 4)x + (2 – 1)y + 7

=7x + y + 7

Combine Like Terms Calculator PEMDAS, BEDMAS, BODMAS, GEMDAS, MDAS

There are few exceptions and few rules of Combine like terms in Combining like terms calculator. PEMDAS is an acronym that can assist you in remembering the order of operations when solving math problems. “Please Excuse My Dear Aunt Sally,” as PEMDAS is sometimes abbreviated, is a common expression. However, the PEMDAS acronym is formed by the initial letter of each word in the phrase. Meanwhile, working from left to right, solve math questions using the normal mathematical sequence of operations:

However, parentheses, brackets, and grouping – identify and answer expressions in parentheses first, working from left to right in the equation; if you have nested parentheses, work from the innermost to outermost.

Similarly, exponents and Roots – compute all exponential and root expressions in the equation from left to right.

Next, answer both multiplication AND division expressions as they appear in the equation, working left to right in the equation. This is where you’ll begin with the MDAS rule.

Addition and Subtraction – Solve both addition and subtraction expressions as they appear in the problem, working from left to right.

Combine Like Terms Calculator Caution

In the Combine like term calculator, multiplication isn’t always done first, and division isn’t always done last. Multiplication and division are carried out from left to right in the equation.

It is not always the case that addition comes before subtraction. However, subtraction and addition are done in the order they appear in the equation, from left to right.

The order “MD” (DM in BEDMAS) is commonly misunderstood to suggest that Division comes before Multiplication (or vice versa). Multiplication and division, on the other hand, have the same precedence. In other words, from left to right, multiplication and division are done in the same step. 4/2*2 equals 4, yet 4/2*2 does not equal 1.

A similar mistake can be made with “AS,” because addition and subtraction have the same priority and are done in the same step from left to right. 5 – 3 + 2 Equals 4, for example, therefore 5 – 3 + 2 does not equal 0.

However, PEMDAS may be written as PE (MD) (AS) or BEDMAS could be written as BE (DM) (AS).

Acronyms for the Order of Operations

However, order of operations acronyms indicates that you should answer equations in this order, working from left to right in the problem.

Full Forms of PEMDAS, BODMAS, GEMDAS, MDAS, BEDMAD

Meanwhile, PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) is an acronym for “Parentheses, Exponents, Multiplication and Division, Addition and Subtraction.”

However, the acronyms for the order of operations are BEDMAS, BODMAS, and GEMDAS. Similarly, “Brackets” is the same as parentheses in these acronyms, and “order” is the same as exponents. “Grouping” in GEMDAS is equivalent to parentheses or brackets.

However, “Brackets, Exponents, Division and Multiplication, Addition and Subtraction” is the acronym for “Brackets, Exponents, Division and Multiplication, Addition and Subtraction.”

BEDMAS is a bit like BODMAS.

Meanwhile, “Brackets, Order, Division and Multiplication, Addition and Subtraction” is what BODMAS stands for.

And “Grouping, Exponents, Multiplication, Division, Addition and Subtraction” is what ‘GEMDAS’ stands for.

However, MDAS is a combination of the acronyms listed above. “Multiplication, Division, Addition, and Subtraction” is what it stands for.

Combine Like Terms Calculator Associativity

Meanwhile, Left-associative operations include multiplication, division, addition, and subtraction. This means that while solving multiplication and division expressions, you work from the left to the right side of the problem. When solving addition and subtraction expressions, you go from left to right in the same way.

Left-associativity examples include:

a / b * c = (a / b) * c

a + b – c = (a + b) – c

However, Right-associative exponents and roots or radicals are solved from right to left.

Right-associativity examples include:

2^3^4^5 = 2^(3^(4^5))

2r3^(4/5) = 2r(3^(4/5))

When working with nested parentheses or brackets, start with the innermost parentheses or bracket expressions and work your way out. However, follow the rest of the PEMDAS order for each expression within parentheses: Exponents and radicals come first, followed by multiplication and division, and ultimately addition and subtraction.

After solving for parentheses, exponents, and radicals, and before adding and subtracting, you can solve multiplication and division in the same stage of the math problem. However, multiplication and division should be done from left to right. After parenthesis, exponents, roots, and multiplying/dividing, solve addition and subtraction last. To add and subtract, go from left to right once more.

Combine Like Terms Calculator Rules

To solve equations, the Combine like terms calculator uses established rules.

(+) Addition Operations Rules

If the signs are identical, preserve the sign and double the numbers.

(-) + (-) = (-) (+) + (+) = (+)

-21 + -9 = – 30 (+7) + (+13) = (+20)

If the signs disagree, subtract the smaller number from the bigger number while keeping the larger number’s sign.

(-Large) + (+Small) = (-) (-Small) + (+Large) = (+)

(-13) + (+5) = (-8) (-7) + (+9) = (+2)

(-) Subtraction Operations Rules

Keep the first number’s sign. Substitute additional signs for all of the following subtraction signs. However, follow the guidelines for subsequent problems by changing the sign of each number that follows such that positive becomes negative and negative becomes positive.

(-) – (-) = (-) – (+) = (+) – (-) =

(-15) – (-7) = (-5) – (+6) = (+4) – (-3) =

(-15) + (+7) = (-8) (-5) + (-6) = (-11) (+4) + (+3) = (+7)

(* or ×) Multiplication Operations Rules

However, a positive outcome is obtained by multiplying a negative by a negative or a positive by a positive. Meanwhile, a negative result is obtained by multiplying a positive by a negative or a negative by a positive.

(-) * (-) = (+) | (+) * (+) = (+) | (+) * (-) = (-) | (-) * (+) = (-)

-10 * -2 = 20 10 * 2 = 20 10 * -2 = -20 -10 * 2 = -20

(-) × (-) = (+) | (+) × (+) = (+) | (+) × (-) = (-) | (-) × (+) = (-)

-10 × -2 = 20 10 × 2 = 20 10 × -2 = -20 -10 × 2 = -20

(÷ or / ) Division Operations Rules

Again, dividing a negative by a negative or a positive by a positive yields a positive result, similar to multiplication. When you divide a positive by a negative or a negative by a positive, the outcome is negative.

(-) / (-) = (+) | (+) / (+) = (+) | (+) / (-) = (-) | (-) / (+) = (-)

-10 / -2 = 5 10 / 2 = 5 10 / -2 = -5 -10 / 2 = -5

(-) ÷ (-) = (+) | (+) ÷ (+) = (+) | (+) ÷ (-) = (-) | (-) ÷ (+) = (-)

-10 ÷ -2 = 5 10 ÷ 2 = 5 10 ÷ -2 = -5 -10 ÷ 2 = -5

Combine Like Terms Calculator Properties

Variables can be used to represent a wide range of numbers.
Meanwhile, a constant is a number that isn’t changed by a variable in any way.
Numbers, variables, grouping symbols, and operation symbols make up algebraic expressions. However, a term is a component of an algebraic expression that is made up of numerous elements.
Hence, we represent the numerical part of a phrase by a numerical coefficient (or coefficient). The numerical coefficient in the word 5x, for example, is 5. This indicates that the variable x has been multiplied by 5.
However, if a phrase does not have a numerical coefficient, we presume it has a coefficient of 1. For example, x is equal to 1x, whereas -x is equal to -1x.

Combine Like Terms and Simplify Examples

Example: 1

Facilitate a representation

4x² +3x +4y +8x +9x²

Solution:

Collect and add similar phrases that result in:

9x² +4x² +8x +3x +4y

= 13x² +11x +4y.

We may deduce that the phrases have the same variables raised to the same exponent based on this example.

Example: 2

Facilitate

2xy + 4x² +3yx + 5y² +16x².

Solution:

The expressions 2xy and 3yx, as well as 4x² and 16x², have identical variables in this case. Because of the commutative property of multiplication, 2xy and 3yx are the same.

Therefore, 2xy+3yx=5xy & 4x² +16x² =20x²

Hence, 2xy +4x² +3yx+ 5y²+ 16x²

=5xy +20x² + 5y²

Example: 3

Facilitate

5m + 14m – 6n– 5n + 2m

Solution:

Rewrite the statement so that the terms that are similar are close to one another.

5m + 14m – 6n – 5n + 2m

Mix the coefficients.

(5+14+2)m + (−6+−5)n

=21m–11n

Example: 4

Facilitate

3x² + 3x – 4 – x² + x + 9

Solution:

Sort the terms by their degree on head

=3x² +3x –4 –x² + x+ 9

=(3x²–x²) + (3x+x) + (–4+9)

=(3–1) x² + (3+1) x + (5)

=(2) x² + (4) x + 5

=2x² + 4x +5

Example: 5

Facilitate

(10x³ –14x² +3x –4x³ +4x –6)

Solution:

Sort terms by their magnitudes or exponentials

=12x³ –14x² +3x – 4x³ + 4x– 6

=(12x³ –4x³) + (–14x²) + (3x+4x) – 6

=8x³ –14x² + 7x–6

Example: 6

Facilitate

[(6x–8)–2x]–[(12x–7)–(4x–5)]

Solution:

From the inside out, simplify

=[(6x–8)–2x]–[(12x–7)–(4x–5)]

=[6x–8–2x]–[12x–7–1(4x)–1(–5)]

=[6x–2x–8]–[12x–7–4x+5]

=[4x–8]–[12x–4x–7+5]

=4x–8–[8x–2]

=4x–8–1[8x]–1[–2]

=4x–8–8x+2

=4x–8x–8+2

=–4x–6

Some Frequently Asked Questions about Combine Like Terms Calculator

How do you combine like terms in a Combination like terms calculator?

Simplifying algebraic expressions is a frequent approach. We add the coefficients of phrases like 2x and 3x when combining them. As an example,

2x+3x=(2+3)x=5x

What are combine like terms in a Combine like terms calculator?

Terms with identical variable portions (same variable(s) and exponent(s)) are referred to as “like terms.” You combine “like terms” by keeping the “like term” and adding or subtracting the numerical coefficients when simplifying using addition and subtraction. 3x + 4x Equals 7x, for example.

Are 5a and 5b like terms?

Yes. Unlike terms are those that have distinct algebraic factors.

Are 2×2 and like terms or not like terms?

Like terms have the same variable and power, whether it’s x, x3, y, or no variable at all. Similarly, 2x and 2×2 are not equivalent words since the variables are increased to different powers. It’s easy to get this mixed up with multiplying exponents.

Are XY and YX like terms?

Terms satisfy the associative property of multiplication, which means that xy and yx, as well as xy2 and y2x, are like terms.

What are “like terms” infractions in a Combine like terms calculator?

Individual terms with the same variable are referred to as “like terms.” In any “like words,” the variable is also raised to the same power. For instance, the phrases 3x and 10x are similar (both have the variable x, raised to the 1st power).

How do you add fractions and fractions in a Combine like terms calculator?

Multiply each fraction’s numerator by the denominator of the other:

⅓ + ⅖

1*5 = 5

2*3 = 6

To find the numerator of the solution, add the results:

5 + 6 = 11

To find the answer’s denominator, multiply the two denominators together.

Simply multiply the denominators of the two fractions to get the denominator:

3*5 = 15

The answer’s denominator is 15.

Make a fraction out of your answer.

⅓ + ⅖ = 11/15