Combining Like Terms Calculator

This Combining Like Terms Calculator is used to simplify algebraic expressions by combining like terms. Enter an expression into the input box, and the calculator identifies terms with the same variables and exponents, then adds or subtracts their coefficients according to the standard sign rules. It is useful for students checking homework or anyone who wants to simplify an algebraic expression.

What are Like Terms?

Like terms are algebraic terms containing the exact same variable raised to the same power. In the same terms, only the numerical coefficient can differ from one another.

How to Identify Like Terms?

Here's the rule: for terms to be "like" terms, they must have the same variable(s) raised to the same power(s). Here is a table of comparison:

Like Terms:	NOT Like Terms:
\(3x\) and \(7x\) → both have \(x\) to the first power	\(3x\) and \(3y\) → different variables
\(5y^2\) and \(-2y^2\) → both have \(y^2\)	\(5x\) and \(5x^2\) → same variable, different exponents
\(8ab\) and \(4ab\) → both have \(ab\)	\(2xy\) and \(2x\) → different variable combinations
\(12\) and \(-5\) → both are constants (no variables)	\(7a^2b\) and \(7ab^2\) → exponents are on different variables

What Are the Components of Like Terms?

To understand like terms, identify the parts of a term, for example, 4x²:

Coefficient
Exponent
Variable or Base

like terms

How to Use this Combining Like Terms Calculator?

Using this calculator takes just a few steps:

Enter an expression or copy/paste your algebraic expression, including coefficients, variables, exponents, parentheses, and fractions.
Press CALCULATE to get an instant and step-by-step solution.
Review the result of the given expression along with a step-by-step solution of how each term was combined.

How to Combine Like Terms?

To combine like terms, you need to follow these steps:

Group the Like Terms: Find terms with the same variables and exponents.
Combine Their Coefficients: Add or subtract their coefficients while keeping the variables unchanged.
Write the simplified expression: Combine the simplified terms and constants to get the final expression.

Example # 1:

3x^2 + 5x - 2x^2 + 4x

Group the like terms: (3x^2 - 2x^2) + (5x + 4x)

Combine: x^2 + 9x

Write the simplified expression: x^2 + 9x

Example # 2:

8m³ - 3m² + 2m³ + 5m²

Group the like terms: (8m³ + 2m³) + (-3m² + 5m²)

Combine: 10m³ + 2m²

Write the simplified expression: 10m³ + 2m²

Example # 3:

6p² + 4q - 3p² + 7q

Group the like terms: (6p² - 3p²) + (4q + 7q)

Combine: 3p² + 11q

Write the simplified expression: 3p² + 11q

What are Rules For Operations On Like Terms?

Follow these simple rules:

Operation Sequence Rules:

When simplifying the expression by combining similar terms, the order of operations is:

PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction
BEMDAS: Brackets, Exponents, Multiplication, Division, Addition, Subtraction
BODMAS: Brackets, Order, Division, Multiplication, Addition, Subtraction
GEMDAS: Grouping, Exponents, Division, Multiplication, Addition, Subtraction
MDAS: Multiplication, Division, Addition, Subtraction

Operator Associativity:

Multiplication, Division, Addition, and Subtraction are left-associative (calculate left to right). Exponents are right-associative.

Left-Associative (calculate left to right): X / Y * Z = (X / Y) * Z, X + Y - Z = (X + Y) - Z

Right-Associative (calculate right to left): x^y^z^n = x^(y^(z^n))

You don’t need to worry about left or right associativity while working with the combining like terms calculator. The tool automatically handles associativity and operator precedence. So you can focus on solving problems, not on order of operations

Addition (+):

If the signs are the same, keep the sign and add the coefficients; if the signs are different, subtract the smaller coefficient from the larger one and keep the sign of the larger coefficient.

(-) + (-) = (-)	(+) + (+) = (+)
(-15x) + (-5x) = -20x	(+12x) + (+8x) = +20x
(-15x) + (+5x) = -10x	(-6y) + (+8y) = +2y

Subtraction (-):

Keep the first term’s sign, change the remaining terms’ signs, then apply addition rules:

(-) - (-)	(-) - (+)	(+) - (-)
(-15x) - (-5x)	(+12x) - (+8x)	(+5x) - (-6x)
-15x + 5x = -10x	+12x - 8x = +4x	+5x + 6x = +11x

Multiplication (*):

Multiplication rules for signs:

(-) * (-) = (+)	(-) * (+) = (-)	(+) * (-) = (-)	(+) * (+) = (+)
(-5)*(-5)=25	(-5)*(+8)=-40	(+5)*(-6)=-30	(+5)*(+7)=35

Division (÷):

Division follows the same rules as multiplication:

(-) / (-) = (+)	(-) / (+) = (-)	(+) / (-) = (-)	(+) / (+) = (+)
(-10)/(-10)=+1	(-10)/(+2)=-5	(+15)/(-3)=-5	(+7)/(+7)=+1

Combining Like Terms Calculator

What are Like Terms?

What Are the Components of Like Terms?

How to Use this Combining Like Terms Calculator?

How to Combine Like Terms?

Example # 1:

Example # 2:

Example # 3:

What are Rules For Operations On Like Terms?

Operation Sequence Rules:

Operator Associativity:

Addition (+):

Subtraction (-):

Multiplication (*):

Division (÷):

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