Question

(x^2+1)^2-(x^2-5)^2

(4x^2-25)^2-(2x-5)^2 help

Answer 1

1.

(x^2 +1)^2 -(x^2 -5)^2 =

= x^4 + 2x^2 +1 -(x^4 -10x^2 + 25) =

= x^4 + 2x^2 +1 - x^4 +10x^2 - 25 =

= 12x^2 - 24 =

= 12(x^2 - 2)

2.

(4x^2 - 25)^2 -(2x -5)^2 =

= [(2x+5)(2x-5)]^2 -(2x-5)^2 =

= (2x+5)^2 *(2x-5)^2 -(2x-5)^2 =

=(2x-5)^2 * [(2x+5)^2 -1] =

=(2x-5)^2 *(4x^2 +20x+25-1) =

=(2x-5)^2 *(4x^2 +20x +24)=

=(2x-5)^2 * 4(x^2 +5x+6) =

= 4(2x-5)^2 *(x+2)(x+3)