Algebra Practice

Combining Like Terms Practice Test

Combine coefficients accurately across integers, fractions, decimals, powers, and distributed expressions.

Combining Like Terms Practice Test

20 varied questions on identifying and combining like terms.

Instant feedback · Worked explanations
After the test · term sorting

Combining like terms is a classification problem before it is an arithmetic problem

The coefficients may be positive, negative, fractional, or decimal. That does not decide whether terms can be combined. First compare the complete variable part — every variable and every exponent. Only after two terms belong to the same algebraic family should their coefficients be added or subtracted.

x and x²Multivariable termsSigned coefficients FractionsDecimalsDistribution firstPolynomial subtraction
Term identity cards

A term has two layers: coefficient and variable identity

The coefficient tells how many of that term you have. The variable part tells what kind of term it is.

Term A
7x²y
coefficient: 7identity: x²y
Term B
−4x²y
coefficient: −4identity: x²y
Term C
3xy²
coefficient: 3identity: xy²

A and B can combine because their identities match. C stays separate because xy² is different from x²y.

Term-family board

Sort a long expression into families before touching the coefficients

For a mixed polynomial, visual grouping is often faster and safer than combining terms in the order they appear.

x² terms
5x²−2x²½x²
x terms
7x−3x
constants
4−92
A clean rewrite might be (5 − 2 + ½)x² + (7 − 3)x + (4 − 9 + 2). The variables remain unchanged while the coefficients are combined.
Coefficient ledger

After classification, the algebra becomes signed arithmetic

8x − 3x + 5x
(8 − 3 + 5)x
10x

Notice what did not change: the variable x. Combining like terms changes the numerical multiplier, not the exponent, variable name, or variable product.

Addition/subtraction of like terms acts on coefficients. Multiplication of powers is a different operation with different exponent rules.
Multivariable sorting

With several variables, the entire exponent pattern must match

Order can be standardized, but the variables and their powers must represent the same monomial.

Like terms
2ab² − 5ab² + ½ab²
= (2 − 5 + ½)ab²
= −5/2 ab²
Unlike terms
4a²b + 3ab²
cannot be combined
Fraction and decimal station

The variable decision stays the same even when the coefficient arithmetic changes format

Fractional coefficients

3/4 x − 1/6 x
= 9/12 x − 2/12 x
= 7/12 x

Find a common denominator for the coefficients; leave x untouched.

Decimal coefficients

2.75y − 0.8y + 1.05y
= 3.00y

Align the decimal arithmetic carefully, but the like-term rule does not change.

Distribution before collection

Parentheses can hide like terms that do not exist visibly yet

Remove grouping first; then perform the term classification.

Original3(2x − 4) + 5x
Distribute6x − 12 + 5x
Collect(6x + 5x) − 12
Result11x − 12
Why like terms matter in models

Geometry expressions often create repeated copies of the same algebraic quantity

A rectangle has two lengths and two widths. Combining like terms turns that repeated structure into a simpler perimeter expression.

P = 2(3x + 2) + 2(x + 5)
P = 6x + 4 + 2x + 10
P = 8x + 14
Stop signs: do not combine

Some pairs look similar enough to tempt you, but they belong to different families

x vs x² Different exponents mean different variable identities.
xy vs x + y A product term and two separate terms are not the same structure.
x²y vs xy² The same letters are present, but the exponent pattern is different.
Combination audit

Four plausible-looking errors to reject immediately

3x + 4x = 7x² 3x + 4x = 7x

The coefficients add; the variable part stays x.

2x² + 5x = 7x³ 2x² + 5x stays as written.

x² and x are unlike terms, so there is no legal coefficient combination.

4a + 3b = 7ab 4a + 3b stays as written.

a-terms and b-terms are different families.

−2x + 5x = −7x −2x + 5x = 3x

Keep the original signs when combining the coefficients: −2 + 5 = 3.

Use the score diagnostically

A missed question usually belongs to one of four different failure points

Classifying the mistake tells you what to review next instead of memorizing one corrected expression.

IdentityVariables and exponents were not matched correctly.
SignsThe term family was right, but the coefficient sign was lost.
Coefficient arithmeticFractions, decimals, or integers were combined incorrectly.
Hidden termsDistribution or polynomial subtraction had to happen first.