Grades Grade 7 Expressions & EquationsFactoring & Expanding Linear Expressions

Factoring & Expanding Linear Expressions

✏️ Expressions & Equations

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Factoring & Expanding Linear Expressions

Use the distributive property to factor out common terms or expand parentheses.

The distributive property lets you rewrite expressions in two ways: expanding (removing parentheses) or factoring (inserting parentheses by pulling out a common factor). Both forms are equivalent.

a(b + c) = ab + ac \qquad (\text{expanding})

ab + ac = a(b + c) \qquad (\text{factoring})

📦Expanding then combining like terms

Simplify 3(2x − 5) + 4x

Step 1 — Expand: 6x − 15 + 4x
Step 2 — Combine like terms: (6x + 4x) − 15 = 10x − 15
Step 3 — Factor if needed: 5(2x − 3)

3(2x - 5) + 4x = 6x - 15 + 4x = 10x - 15 = 5(2x - 3)

Finding the GCF to factor:

1List the coefficients and find the Greatest Common Factor (GCF)

2Divide every term by the GCF

3Write the GCF outside parentheses and the divided terms inside

4Check by expanding back out

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Remember This!

Like terms must have the same variable AND the same exponent. 3x and 5x are like terms; 3x and 5x² are not.

✏️ Try It!

Factor 12x + 18 completely.

Practice with CalcVerse

🔍Factors, GCF & LCM ⚡Exponent Rules

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