Question

Multiply and collect like terms: (5m – 3)(m + 2).

Answer 1

The expression (5m – 3)(m + 2) is multiplied using the FOIL method, resulting in 5m^2 + 10m – 3m – 6. After combining like terms, the simplified expression is 5m^2 + 7m – 6.

Step-by-step explanation:

To multiply and collect like terms for the expression (5m – 3)(m + 2), we use the distributive property (also known as the FOIL method). We multiply each term in the first parenthesis by each term in the second parenthesis.

Here are the steps:

1. Multiply the first terms: 5m × m = 5m2.
2. Multiply the outer terms: 5m × 2 = 10m.
3. Multiply the inner terms: –3 × m = –3m.
4. Multiply the last terms: –3 × 2 = –6.

Next, we combine the like terms:

• 5m2 (from step 1)
• 10m – 3m = 7m (from step 2 and 3 combined)
• –6 (from step 4)

Therefore, the fully simplified expression is 5m2 + 7m – 6.