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Combining Like Terms Calculator

Write down the algebraic expression, and the calculator will combine identical terms (if any) in it.

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Combine Like Terms Calculator

The Combine Like Terms calculator helps simplify algebraic expressions by combining like terms. An algebraic expression consists of both like and unlike terms. Combining like terms makes expressions easier to understand and work with.

Components of a Term

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

Coefficient
Exponent
Variable or Base

like terms

What Does It Mean to Combine Like Terms?

Consider 3x² and 4x². Both have the same variable and exponent ("x" and 2), but different coefficients. Adding them gives:

3x² + 4x² = 7x²

This is combining like terms. The calculator can simplify expressions of any length.

Like Term Operation Sequence Rules

When simplifying expressions, the order of operations is crucial:

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 (subset of above)

Operator Associativity

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

Left-Associative: X / Y * Z = (X / Y) * Z, X + Y - Z = (X + Y) - Z
Right-Associative: x^y^z^n = x^(y^(z^n))

Rules for Operations on Like Terms

Addition (+)

Same sign: keep the sign, add coefficients

(-) + (-) = (-)	(+) + (+) = (+)
(-15x) + (-5x) = -20x	(+12x) + (+8x) = +20x

Different signs: subtract smaller from larger, keep the sign of the larger coefficient

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

How the Combine Like Terms Calculator Works

Input:

Enter coefficients, variables, and operators.
Include fractions, monomials, polynomials, or exponential terms.
Press Calculate.

Output:

All like terms are combined according to operations.
Step-by-step solution displayed for clarity.
Press Recalculate to adjust inputs.

FAQs

How do you combine like terms to create an equivalent expression?

Add coefficients of like terms. Example: 3x + 5x = 8x

What is the sequence of solving operations?

Follow order: brackets → division → multiplication → addition → subtraction.

Conclusion

Like terms have the same variables and exponents but may have different coefficients. The Combine Like Terms calculator helps organize and simplify polynomials efficiently.

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