Question

problem 17
distribute this expression and select the simplified answer.
$(x^2 - 2)(x + 4)$
a. $x^3 + 2x^2 + (-4x) + (-8)$
b. $x^2 - 2x + 8$
c. $x^2 + x + 2$
d. $x^3 + (-8x^2) + 4x + (-2)$
e. $x^3 + 4x^2 + (-2x) + (-8)$

Explanation:

Step1: Apply distributive property

Multiply each term in the first binomial by each term in the second binomial:
\( (x^2 - 2)(x + 4) = x^2 \cdot x + x^2 \cdot 4 + (-2) \cdot x + (-2) \cdot 4 \)

Step2: Simplify each product

Simplify each term:
\( x^2 \cdot x = x^3 \), \( x^2 \cdot 4 = 4x^2 \), \( (-2) \cdot x = -2x \), \( (-2) \cdot 4 = -8 \)

Step3: Combine terms

Combine the simplified terms:
\( x^3 + 4x^2 + (-2x) + (-8) \) (which matches option E when written as \( x^3 + 4x^2 + (-2x) + (-8) \))

Answer:

E. \( x^3 + 4x^2 + (-2x) + (-8) \)