Question

Simplify the expression 5(x - 3)(x^2+4x + 1).

A. 5x^3-75x^2+25-15
B. 5x^3+25x^2-75x-15
C. 5x^3+x^2-11x-3
D. 5x^3+5x^3-55x-15

Answer 1

Down below (I believe there may be a typo in answer choice D. I think it's supposed to be 5x^3 + 5x^2. The typo being the three shown in the answer choice.

Explanation:

First, distribute 5 to the (x - 3)

(5x - 15)

Then, distribute (5x - 15) to (x^2 + 4x + 1)

5xx^2 + 5x * 4x + 5x * 1 - 15x^2 - 15 * 4x - 15 * 1

Simplify:

5x^3 + 5x^2 - 55x - 15

Hope this helps!

Answer 2

`\bf 5(x-3)(x^2+4x+1) \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} x-3\\ * ~~5\\ \cline{1-1} 5x-15 \end{array}\qquad \qquad \begin{array}{llll} x^2+4x+1\\ * ~~5x-15\\ \cline{1-1} 5x^3+20x^2+5x\\ -15x^2-60x-15 \end{array} \\\\\\ 5(x-3)(x^2+4x+1)\implies 5x^3+20x^2+5x-15x^2-60x-15 \\\\\\ 5x^3+20x^2-15x^2+5x-60x-15\implies 5x^3+5x^2-55x-15`