How to Use the Distributive Property? (+FREE Worksheet!)
To solve expressions in the form of \(a(b + c)\), we need to use the distributive property or the distributive property of multiplication.
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Related Topics
- How to Translate Phrases into an Algebraic Statement
- How to Simplify Variable Expressions
- How to Simplify Polynomial Expressions
- How to Evaluate One Variable
- How to Evaluate Two Variables
Step by step guide to use the distributive property correctly
- Distributive Property:
\(\color{blue}{a \ (b \ + \ c)=ab \ + \ ac} \)
For education statistics and research, visit the National Center for Education Statistics.
The Distributive Property – Example 1:
Simplify. \((- \ 2)(x \ – \ 3)=\)
Solution:
Use Distributive Property formula: \(a \ (b \ + \ c)=ab \ + \ ac \)
\((-2)(x-3)=-2x+6\)
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The Distributive Property – Example 2:
Simplify. \((5)(6x\ – \ 3)=\)
Solution:
Use Distributive Property formula: \(a \ (b \ + \ c)=ab \ + \ ac \)
\((5)(6 x – \ 3)=30x\ – \ 15 \)
The Distributive Property – Example 3:
Simplify. \((5x-3)(–5)=\)
Solution:
Use Distributive Property formula: \(a(b+c)=ab+ac \)
\((5x-3)(–5)=-25x+15 \)
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The Distributive Property – Example 4:
Simplify \((-8)(2x-8)=\)
Solution:
Use Distributive Property formula: \(a(b+c)=ab+ac \)
\((-8)(2x-8)=-16x+64\)
Exercises for Using the Distributive Property
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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