Question

(2x+4)^4-(2x^2+5x+2)^2-12 (x+2)^4

Answer 1

2х^4+ 4^4- 2х^4-5х^2+4-12х^4+24^4
4^4+4-24^4
-17х^2-20^4+4

Answer 2

To simplify the expression (2x+4)^4 - (2x^2+5x+2)^2 - 12(x+2)^4, let's break it down step by step:

Step 1: Expand the terms (2x+4)^4 = (2x+4)(2x+4)(2x+4)(2x+4) = (2x)^4 + 4(2x)^3(4) + 6(2x)^2(4)^2 + 4(2x)(4)^3 + (4)^4 = 16x^4 + 64x^3 + 96x^2 + 64x + 256

(2x^2+5x+2)^2 = (2x^2+5x+2)(2x^2+5x+2) = (2x^2)(2x^2) + (2x^2)(5x) + (2x^2)(2) + (5x)(2x^2) + (5x)(5x) + (5x)(2) + (2)(2x^2) + (2)(5x) + (2)(2) = 4x^4 + 20x^3 + 12x^2 + 20x^3 + 25x^2 + 10x + 4x^2 + 10x + 4 = 4x^4 + 40x^3 + 41x^2 + 20x + 4

12(x+2)^4 = 12(x+2)(x+2)(x+2)(x+2) = 12(x^2 + 4x + 4)(x^2 + 4x + 4) = 12(x^2)(x^2) + 12(x^2)(4x) + 12(x^2)(4) + 12(4x)(x^2) + 12(4x)(4x) + 12(4x)(4) + 12(4)(x^2) + 12(4)(4x) + 12(4)(4) = 12x^4 + 96x^3 + 192x^2 + 96x^3 + 384x^2 + 768x + 192x^2 + 768x + 768 = 12x^4 + 192x^3 + 768x^2 + 960x + 768

Step 2: Substitute the expanded terms back into the original expression (2x+4)^4 - (2x^2+5x+2)^2 - 12(x+2)^4 = (16x^4 + 64x^3 + 96x^2 + 64x + 256) - (4x^4 + 40x^3 + 41x^2 + 20x + 4) - (12x^4 + 192x^3 + 768x^2 + 960x + 768)

Step 3: Combine like terms 16x^4 + 64x^3 + 96x^2 + 64x + 256 - 4x^4 - 40x^3 - 41x^2 - 20x - 4 - 12x^4 - 192x^3 - 768x^2 - 960x - 768 = (16x^4 -