Question

(x+4)(x^2 - 4x + 16) - (x-2)(x^2+2x+4)

Answer 1

\(\left(x+4\right)\left(x^2-4x+16\right)-\left(x-2\right)\left(x^2+2x+4\right)\)

\(=x^3-4x^2+16x+4x^2-16x+64-\left(x^3+2x^2+4x-2x^2-4x-8\right)\)

\(=x^3+\left(-4x^2+4x^2\right)+\left(16x-16x\right)+64-\left(x^3-8\right)\)

\(=x^3+0+0+64-x^3+8\)

\(=\left(x^3-x^3\right)+\left(64+8\right)\)

\(=0+72=72\)

Answer 2

(x + 4)(x² - 4x + 16) - (x - 2)(x² + 2x + 4)

= x³ + 4³ - (x³ - 2³)

= x³ + 64 - x³ + 8

= 72