Algebraic Expressions (Two-step) • Topic 2 of 2

Distributive Property & Factoring

Distributive Property: Multiply a number outside parentheses by each term inside.

a(b + c) = ab + ac

Factoring is the reverse of the distributive property — find the Greatest Common Factor (GCF) and pull it out.

ab + ac = a(b + c)

To factor, ask: what is the largest number/variable that divides all terms evenly?

DISTRIBUTIVE PROPERTY:

    3(2x + 5)
         |
    [split here]
    /          \
  3 x 2x  +  3 x 5
    |              |
   6x         +   15

Answer: 6x + 15

FACTORING (reverse):
  8x + 12
  GCF(8,12) = 4
  = 4(2x + 3)

Solved Examples

Worked Example

Simplify: 5(3x + 4)

Solution5 x 3x + 5 x 4 = 15x + 20

Worked Example

Simplify: 2(4y - 7)

Solution2 x 4y - 2 x 7 = 8y - 14

Worked Example

Factor: 8x + 12

SolutionGCF of 8 and 12 is 4. Factor out 4: 4(2x + 3). Check: 4 x 2x = 8x and 4 x 3 = 12.

Key Points

Distribute to EVERY term inside the parentheses
Factoring = finding GCF and writing as a product
Check your factoring by distributing back
GCF must divide both the coefficient and the variable part

Quick Check — 4 MCQs

Tap an option to check your answer0 / 4

Q1.$a(b+c)=$

Explanation: Distribute $a$.

Q2.$2(x+3)=$

Explanation: $2x+6$.

Q3.Factor $6x+9$:

Explanation: HCF $3$.

Q4.Factoring is the reverse of:

Explanation: Expanding.

Practice more MCQs → 📝 Assignment · 35 marks