The Distributive Property

The Distributive Property

To solve expressions in the form of a(b + c), we need to use the distributive property or the distributive property of multiplication.

Step by step guide to use the distributive property correctly

  • Distributive Property:
    \(\color{blue}{a \ (b \ + \ c)=ab \ + \ ac} \)

Example 1:

Simplify. \((- \ 2)(x \ – \ 3)=\)

Solution:

Use Distributive Property formula: \(a \ (b \ + \ c)=ab \ + \ ac \)
\((-2)(x-3)=-2x+6\)

Example 2:

Simplify. \((5)(6 \ x \ – \ 3)=\)

Solution:

Use Distributive Property formula: \(a \ (b \ + \ c)=ab \ + \ ac \)
\((5)(6 \ x \ – \ 3)=30 \ x \ – \ 15 \)

Example 3:

Simplify. \((5x-3)(–5)=\)

Solution:

Use Distributive Property formula: \(a(b+c)=ab+ac \)
\((5x-3)(–5)=-25x+15 \)

Example 4:

Simplify \((-8)(2x-8)=\)

Solution:

Use Distributive Property formula: \(a(b+c)=ab+ac \)
\((-8)(2x-8)=-16x+64\)

Exercises

Use the distributive property to simplify each expression.

  • \(\color{blue}{– (– 2 – 5x)}\)
  • \(\color{blue}{(– 6x + 2)(–1)}\)
  • \(\color{blue}{(– 5) (x – 2)}\)
  • \(\color{blue}{(– 2x) (– 1 + 9x) – 4x (4 + 5x)}\)
  • \(\color{blue}{3 (– 5x – 3) + 4(6 – 3x)}\)
  • \(\color{blue}{(– 2)(x + 4) – (2 + 3x)}\)

Download The Distributive Property Worksheet

Answers

  • \(\color{blue}{5x + 2}\)
  • \(\color{blue}{6x – 2}\)
  • \(\color{blue}{–5x + 10}\)
  • \(\color{blue}{– 38x^2 – 14x}\)
  • \(\color{blue}{– 27x + 15}\)
  • \(\color{blue}{– 5x – 10}\)

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