Algebra Practice

Algebraic Expressions Practice Test

Simplify, evaluate, translate, factor, and analyze algebraic expressions with one or several variables.

Algebraic Expressions Practice Test

20 varied algebraic-expression questions with worked explanations.

Instant feedback · Worked explanations
After the test · expression strategy

Algebraic expressions become easier when you identify the structure before choosing an operation

An expression can contain coefficients, variables, constants, exponents, parentheses, fractions, and several kinds of terms at once. The safest approach is not to “do something to the x.” First decide whether the task is to simplify, evaluate, expand, factor, compare, or identify a structural feature such as degree.

Like termsDistributionEvaluationPolynomialsGCF factoringDegreeSigned termsFractions
Expression anatomy

Know which part of the expression you are changing

In the expression below, the visible pieces play different roles. Confusing those roles is one of the main reasons unlike terms get combined or exponents get changed incorrectly.

4x² − 3xy + 7
CoefficientThe numerical factor multiplying the variable part, such as 4 in 4x².
Variable partThe letters and exponents. Like terms require this part to match exactly.
ConstantA term with no variable, such as 7. Constants combine only with constants.
Simplification decision path

Do the structural work in a stable order

A consistent order prevents sign errors and makes complicated expressions easier to audit.

1ParenthesesDistribute or simplify inside.
2SignsTrack every negative factor.
3Like termsMatch variables and exponents.
4CoefficientsAdd or subtract only the numbers.
5CheckCompare the original and new forms.
Like-term matrix

Terms combine only when their variable parts are identical

Can be combined

5x²−3x²½x²

Each term has exactly x² as its variable part. Only the coefficients change.

Cannot be combined

5x²5x5xy

The variable parts differ: x², x, and xy are three different algebraic terms.

Negative-distribution lab

A negative factor changes every term inside the parentheses

−3(2x − 5)
−6x + 15
not −6x − 5

Distribution is multiplication. The outside factor multiplies every term inside the parentheses: −3·2x = −6x and −3·(−5) = +15.

When subtracting an entire polynomial, treat the subtraction as multiplication by −1 and change every sign inside.
Evaluation workflow

Substitution is safest when signed values are placed inside parentheses

Suppose an expression must be evaluated at x = −2 and y = 3. Parentheses make the sign of the substituted value explicit.

Expression2x² − 3y
Substitute2(−2)² − 3(3)
Powers2(4) − 9
Result−1
Polynomial addition and subtraction

Line up like terms before combining coefficients

Add polynomials

(3x² + 2x − 4) + (x² − 5x + 7)
= 4x² − 3x + 3

The x² terms, x terms, and constants are combined separately.

Subtract polynomials

(3x² + 2x − 4) − (x² − 5x + 7)
= 3x² + 2x − 4 − x² + 5x − 7
= 2x² + 7x − 11

The subtraction changes the sign of every term in the second polynomial.

Greatest-common-factor factoring

Factoring reverses distribution

For 12x³y + 18x²y², the greatest common monomial contains the greatest numerical factor and every variable factor shared by both terms.

12x³y + 18x²y²
GCF = 6x²y
6x²y(2x + 3y)
Structure check

Some expression questions ask you to identify a feature rather than transform anything

CoefficientRead the numerical factor attached to a term.
Constant termFind the term that has no variable factor.
Degree of a termAdd exponents on its variable factors.
Degree of a polynomialUse the greatest degree among its nonzero terms.
Error lab

Four algebra mistakes that produce believable but non-equivalent expressions

3x + 4x² = 7x³Keep 3x + 4x² unchanged.

Addition does not combine unlike variable parts and does not add exponents.

−2(x − 6) = −2x − 12−2(x − 6) = −2x + 12.

The negative factor multiplies the negative 6, producing a positive term.

x² + x² = x⁴x² + x² = 2x².

Like terms add coefficients. Exponents are not added when terms are added.

(a + b)² = a² + b²(a + b)² = a² + 2ab + b².

Squaring a binomial means multiplying the entire binomial by itself.

Use your score diagnostically

Review the kind of algebraic decision that caused each missed question

A missed expression question is more useful when you classify the error instead of only memorizing the final answer.

Signs & distributionReview negatives outside parentheses and polynomial subtraction.
Like termsCheck whether variable names and exponents match exactly.
EvaluationUse parentheses when substituting negative or fractional values.
StructureReview coefficient, constant, GCF, and degree questions separately.