Question

A) (x+2)(x²-2x+4)-x(x+2)(x-2)​

Answer 1

Ответ:

2x³ + 2x² - 4x + 8.

Пошаговое объяснение:

A) (x+2)(x²-2x+4)-x(x+2)(x-2)​

(x+2)(x²-2x+4) = x(x²-2x+4) + 2(x²-2x+4) = x³ - 2x² + 4x + 2x² - 4x + 8 = x³ + 8

x(x+2)(x-2) = x(x²-2x) - 2x(x-2) = x³ - 2x² - 2x³ + 4x = -x³ - 2x² + 4x

(x+2)(x²-2x+4)-x(x+2)(x-2) = (x³ + 8) - (-x³ - 2x² + 4x) = 2x³ + 2x² - 4x + 8

Answer 2

To simplify the expression:

A) (x+2)(x²-2x+4)-x(x+2)(x-2)

We can start by distributing the terms within each set of parentheses:

(x+2)(x²-2x+4) = x(x²-2x+4) + 2(x²-2x+4) = x³-2x²+4x + 2x²-4x+8 = x³+8

x(x+2)(x-2) = x(x²-2x) - 2x(x²-2x) = x³-2x² - 2x³+4x² = -x³+2x²

Now, substitute these results back into the original expression:

(x+2)(x²-2x+4)-x(x+2)(x-2) = (x³+8) - (-x³+2x²) = x³+8 + x³-2x² = 2x³-2x²+8

So, the simplified form of the expression (x+2)(x²-2x+4)-x(x+2)(x-2) is 2x³-2x²+8.