Question

Спростити вирази: 4) (x-2)(x2+2x+4)+(4-x)(x2+4x+16) 5) y(y+3)(y-3) - (y-5)(y2+5y+25)​

Answer 1

Ответ:

4)56

5)у³-7у²+у+125

Объяснение:

ось так

Answer 2

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

First, let's simplify each term within the parentheses: (x - 2)(x^2 + 2x + 4) = x(x^2 + 2x + 4) - 2(x^2 + 2x + 4) = x^3 + 2x^2 + 4x - 2x^2 - 4x - 8 = x^3 - 8

(4 - x)(x^2 + 4x + 16) = 4(x^2 + 4x + 16) - x(x^2 + 4x + 16) = 4x^2 + 16x + 64 - x^3 - 4x^2 - 16x = -x^3 + 64

Now, let's combine the simplified terms: (x - 2)(x^2 + 2x + 4) + (4 - x)(x^2 + 4x + 16) = x^3 - 8 + (-x^3 + 64) = -8 + 64 = 56

Therefore, the simplified expression is 56.

2. y(y + 3)(y - 3) - (y - 5)(y^2 + 5y + 25)

Let's expand the expression step by step:

y(y + 3)(y - 3) = y(y^2 - 9) = y^3 - 9y

(y - 5)(y^2 + 5y + 25) = y(y^2 + 5y + 25) - 5(y^2 + 5y + 25) = y^3 + 5y^2 + 25y - 5y^2 - 25y - 125 = y^3 - 125

Now, let's subtract the second expression from the first one: y(y + 3)(y - 3) - (y - 5)(y^2 + 5y + 25) = (y^3 - 9y) - (y^3 - 125) = y^3 - 9y - y^3 + 125 = 125 - 9y

Therefore, the simplified expression is 125 - 9y.