Question

Which of the following represents the correct expansion of (x + 2)^5?

A. x5 + 10x4 + 40x3 + 40x2 + 10x +32
B. x5 + 8x4 + 12x3 + 8x2 + x +32
C. x5 + 10x4 + 20x3 + 20x2 + 10x +32
D. x5 + 10x4 + 40x3 + 80x2 + 80x +32

Answer 1

(x + 2)^5 = (x + 2) (x + 2) (x + 2)(x + 2)(x + 2) =
(x2 + 4x + 4)(x2+4x+4)(x+2) = ( x4 + 4x3 + 4x2 + 4x3 + 16x2 + 16x + 4x2 +16x + 16)(x+2) = ( x4 + 8x3 + 24x2 + 32x + 16)(x+2) = ( x5 + 8x4 + 24x3 + 32x2 + 16x + 2x4 + 16x3 + 48x2 + 64x + 32) =
x5 + 10x4 + 40x3 + 80x2 + 80x + 32
Answer D