High School

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------------------------------------------------ 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 :

Answer:

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.

Step-by-step 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!

[tex]\bf 5(x-3)(x^2+4x+1) \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{llll} x-3\\ \times ~~5\\ \cline{1-1} 5x-15 \end{array}\qquad \qquad \begin{array}{llll} x^2+4x+1\\ \times ~~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[/tex]

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