Question

Which expression is equivalent to (x + 2)(3r^2 + 4x - 9)?

a) 3r + x - 9
b) 3r^3 + 4xr - x
c) 3r^3 + 10r - 3 - 18
d) 6r^3 + 8xr - 18r

Answer 1

The expression (x + 2)(3r^2 + 4x - 9) can be simplified using the distributive property. The equivalent expression is 6r^3 + 8xr - 18r.

Step-by-step explanation:

The expression (x + 2)(3r^2 + 4x - 9) can be simplified using the distributive property. To expand this expression, we need to multiply each term in the first set of parentheses by each term in the second set of parentheses.

So, (x + 2)(3r^2 + 4x - 9) = x * 3r^2 + x * 4x + x * (-9) + 2 * 3r^2 + 2 * 4x + 2 * (-9)

Simplifying further, we get 3r^2 * x + 4x * x - 9x + 6r^2 + 8x - 18. Combining like terms, the expression is equivalent to 3r^2x + 4x^2 - 9x + 6r^2 + 8x - 18. Therefore, the correct answer is d) 6r^3 + 8xr - 18r.