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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 (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

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.

FAQ's:

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

Identify like terms
Add or subtract the coefficients
Write the equivalent expression

Example:

Simplify:

4𝑎 + 7𝑎 − 3𝑏 +2𝑏

Step 1: Identify

4𝑎 + 7𝑎 − 3𝑏 +2𝑏

Step 2: Combine like terms

4𝑎 + 7𝑎 = 11𝑎
-3𝑏 +2𝑏 = -𝑏

Step 3: Write simplified expression

11𝑎 - 𝑏

What is the sequence of solving operations?

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

Conclusion:

The like terms are the algebraic terms having the same power and exponents but their coefficients are different. The combine like terms calculator assists to write the polynomial in the perfect order to simplify the calculation.

References:

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