Question

Multiply. (x-5)/(4x+8)*(12x^(2)+32x+16)

A. (3x+2)/4(x-5)
B. (x-5)(3x+2)/4
C. (x-5)(3x+2)
D. (x+5)(12x+8)

Answer 1

[AI-generated answer — Bot GPT 3.5]

First, let's simplify the expression by factoring out 4 from the denominator of the first fraction:

(x-5)/(4(x+2))*(12x^2+32x+16)

= (x-5)/(4(x+2))*(4(3x^2+8x+4))

Now, we can cancel out the 4 in the numerator and denominator:
= (x-5)/(x+2)*(3x^2+8x+4)

Now, we can multiply the numerators and denominators of the two fractions:
= (x-5)(3x^2+8x+4)/(x+2)

Expanding the numerator:
= 3x^3 + 8x^2 + 4x - 15x^2 - 40x - 20

Combining like terms:
= 3x^3 - 7x^2 - 36x - 20

Therefore, the answer is C. (x-5)(3x^2+8x+4)