Grade 7 Expressions: Distributive Property

Distribute with negative coefficients

What You'll Learn

Distribute negatives
Simplify after distributing

📖Distribute

Multiply the number outside by every term inside, and watch the signs: −3(x − 4) = −3x + 12, and −(2x + 5) = −2x − 5. In 7 − 2(x + 3), the minus sign goes with the 2. Then combine like terms. The missing number (?) can be negative: in −7(k + 9) = −7k + ?, the ? is −63.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
Simplify: −4(y − 8) = −4y + ?
1. Distribute −4 (the minus sign goes with the 4): multiply each term inside the parentheses by −4. (−4) × y = −4y and (−4) × (−8) = 32. So −4(y − 8) becomes −4y + 32.
2. Match −4y + 32 to −4y + ?: the missing number is 32.
Answer: 32
Example 2
Simplify: −2(a + 2) = −2a + ?
1. Distribute −2 (the minus sign goes with the 2): multiply each term inside the parentheses by −2. (−2) × a = −2a and (−2) × 2 = −4. So −2(a + 2) becomes −2a − 4.
2. Match −2a − 4 to −2a + ?: the missing number is −4.
Answer: −4
Example 3
Simplify: 9(m − 8) + 8 = 9m + ?
1. Distribute 9: multiply each term inside the parentheses by 9. 9 × m = 9m and 9 × (−8) = −72. So 9(m − 8) becomes 9m − 72.
2. Now you have 9m − 72 + 8.
3. Like terms have the same variable part. Here the m-term is 9m; the number terms are −72 and 8.
4. Combine the number terms: −72 + 8 = −64.
5. So 9(m − 8) + 8 = 9m − 64.
6. Match 9m − 64 to 9m + ?: the missing number is −64.
Answer: −64