Question

Which of these is a correct expansion of (3x – 2)(2x² + 5)?

A. 3x • 2x² + 3x • 5 + (–2) • 2x² + (–2) • 5
B. 3x • 2x² + 3x • 5 + 2 • 2x² + 2 • 5
C. 3x • 2x² + (–2) • 2x² + 2x² • 5 + (–2) • 5

Answer 1

The correct expansion of (3x – 2)(2x² + 5) by distributing each term in the first binomial across the second binomial results in 6x³ + 15x - 4x² - 10, which corresponds to Option A.

Step-by-step explanation:

The correct expansion of (3x – 2)(2x² + 5) is done by distributing each term in the first binomial across each term in the second binomial. This involves using the distributive property, or FOIL method (First, Outer, Inner, Last), to multiply the terms. We do this step by step:

1. Multiply 3x by 2x²: 3x × 2x² = 6x³
2. Multiply 3x by 5: 3x × 5 = 15x
3. Multiply -2 by 2x²: -2 × 2x² = -4x²
4. Multiply -2 by 5: -2 × 5 = -10

Adding these results together, we get:

6x³ + 15x - 4x² - 10, which corresponds to Option A. This is the correct expansion for the given expression.

Option B is incorrect because it incorrectly adds the product of 2 and 2x², and option C also is incorrect as it misrepresents the distribution of the terms.