What you’ll learn
Given a linear expression of the form a(bx + c) with rational a, b, and c, distribute a to both terms and write an equivalent expanded expression.
Key idea
The outside factor multiplies every term inside the parentheses, not just the first one. If a term inside is negative, its sign travels with it during multiplication.
For 4(2x − 3), multiply 4 by 2x and also by −3. That gives 8x − 12. You can check the expansion by substituting a value for x into both forms. Matching values provide a useful check, while the distributive property explains why the forms are equal for every x.
Worked example
Expand the expression using the distributive property.
8(x + 5)
- 8x + 40
Answer: 8x + 40
Quick Check
Analyze the proposed student response. Choose Correct or Incorrect.
-6(x - 8) Student response: -6x + 48