Question

Multiply (x + 2)(3x² + 4x).

a) 3x³ + 10x² + 8x
b) 3x³ + 22x² + 18x
c) 4x³ + 8x²
d) 4x³ + 12x² + 8x

Answer 1

To multiply the binomials (x + 2) and (3x² + 4x), the distributive property is used, resulting in the expression 3x³ + 10x² + 8x, making choice a) the correct one.

Step-by-step explanation:

To multiply the expressions (x + 2) and (3x² + 4x), we use the distributive property, also known as FOIL (First, Outer, Inner, Last) in this scenario. We need to multiply each term in the first expression by each term in the second expression.

1. First: Multiply the first terms of each expression: x * 3x² = 3x³.
2. Outer: Multiply the outer terms: x * 4x = 4x².
3. Inner: Multiply the inner terms: 2 * 3x² = 6x².
4. Last: Multiply the last terms: 2 * 4x = 8x.

Now, combine like terms:

3x³ + (4x² + 6x²) + 8x = 3x³ + 10x² + 8x

The correct choice is a) 3x³ + 10x² + 8x.