Question

(x^2-4)^2+(x^2-6x-16)^2

Answer 1

Ответ:

=x^4-8x^2+16+x^4+36x^2+256-12x^3-32x^2+192x=

=2x^4-4x^2+272=12x^3+192x=

=2x^4-12x^3-4x^2+192x+272

Пошаговое объяснение:

Answer 2

To simplify the expression, let's expand and simplify each term:

1. Expand and simplify (x^2 - 4)^2: (x^2 - 4)^2 = (x^2 - 4)(x^2 - 4) = x^2(x^2) - 4(x^2) - 4(x^2) + 4(4) = x^4 - 8x^2 + 16

2. Expand and simplify (x^2 - 6x - 16)^2: (x^2 - 6x - 16)^2 = (x^2 - 6x - 16)(x^2 - 6x - 16) = x^2(x^2) - 6x(x^2) - 16(x^2) - 6x(x) + 36x^2 + 96x - 16(x) + 96x + 256 = x^4 - 6x^3 - 16x^2 - 6x^2 + 36x^2 + 96x - 16x + 96x + 256 = x^4 - 6x^3 + 14x^2 + 176x + 256

Now, let's combine the simplified terms:

(x^2 - 4)^2 + (x^2 - 6x - 16)^2 = (x^4 - 8x^2 + 16) + (x^4 - 6x^3 + 14x^2 + 176x + 256) = 2x^4 - 6x^3 + 6x^2 + 176x + 272

Therefore, the simplified expression is 2x^4 - 6x^3 + 6x^2 + 176x + 272.