Question

factorise x4 + 2x3y - 2xy3 - y4

Answer 1

x4+2x3y-2xy3-y4
➡2 (x×2+x×3y-xy-y×2)
➡2(2x+3xy-xy-2y)
➡2(2x+2xy-2y)
➡2×2(x+xy-y
➡4 (x+xy-y)

Answer 2

Answer:

The factories form is $x^4 + 2x^3y - 2xy^3 - y^4=(x+y)^3(x-y)$

Step-by-step explanation:

Given : Expression $x^4 + 2x^3y - 2xy^3 - y^4$

To find : Factories the expression ?

Solution :

We can write the expression as

$x^4 + 2x^3y - 2xy^3 - y^4$

$=(x^2)^2-(y^2)^2+ 2x^3y - 2xy^3$

$=(x^2+y^2)(x^2-y^2)+2xy(x^2-y^2)$

$=(x^2-y^2)(x^2+y^2+2xy)$

$=((x+y)(x-y))(x+y)^2$

$=(x+y)^3(x-y)$

Therefore, The factories form is $x^4 + 2x^3y - 2xy^3 - y^4=(x+y)^3(x-y)$