Expressions & Equations
GradesSixth GradeExpressions & EquationsAlgebraic Expressions with Variables & Exponents

Algebraic Expressions with Variables & Exponents

📐 Expressions & Equations
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Algebraic Expressions with Variables & Exponents

Variables are just unknown numbers waiting to be found.

An algebraic expression contains numbers, variables (letters that represent unknown values), and operations. Unlike equations, expressions have no equal sign. Evaluating an expression means substituting a given value for each variable and computing the result. Exponents tell you how many times to use the base as a factor.

Expression vs. Equation

Expression: 3x + 5 (no = sign)Equation: 3x + 5 = 14 (has = sign)Expressions are simplified or evaluatedEquations are solved

Exponent Rules

x² means x × xx³ means x × x × x2³ = 8 (base 2, exponent 3)5² = 25 (base 5, exponent 2)

When evaluating, always substitute the value in parentheses, then apply order of operations.

3x2+2x−5 when x=4:3(16)+2(4)−5=48+8−5=513x^2 + 2x - 5 \text{ when } x = 4: \quad 3(16) + 2(4) - 5 = 48 + 8 - 5 = 51
🧮Evaluating Expressions
Evaluate 2a² − b when a = 3 and b = 5:
Step 1: Substitute → 2(3)² − 5
Step 2: Exponent → 2(9) − 5
Step 3: Multiply → 18 − 5
Step 4: Subtract → 13
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Remember This!

Always place substituted values in parentheses: write 2(3)² not 23². This prevents order-of-operations errors, especially with negative numbers.

✏️ Try It!

Evaluate 4x² − 3 when x = 2.

Take Quiz 📝 — 25 Questions