Question

(y+1)^3-(y-1)^3 factorize the following polynomial

Answer 1

Explanation:

Let y + 1 be a and y - 1 be b.

$\mathsf{a^3-b^3}$

$\mathsf{=a^3-b^3-3ab(a-b)+3ab(a-b)}$

$\mathsf{=(a-b)^3+3ab(a-b)}$ [by formula]

$\mathsf{=(a-b)[(a-b)^2+3ab]}$

$\mathsf{=(a-b)(a^2-2ab+b^2+3ab)}$ [by formula]

$\mathsf{=(a-b)(a^2+ab+b^2)}$

$\mathsf{=[(y+1)-(y-1)][(y+1)^2+(y+1)(y-1)+(y-1)^2]}$

$\mathsf{=(2)(y^2+2y+1+y^2-1+y^2-2y+1)}$

$\mathsf{=(2)(3y^2+1)}$

$\mathsf{=6y^2+2}$

Answer: 6y^2 + 2

I hope this helps. :D