Question

Factorise
(X+1)^2 - (y-1)^2

Answer 1

Hey

Here is your answer,

By using the identity ,

(a+b)^2 = a^2 + b^2 + 2ab
(a-b)^2 = a^2 + b^2 - 2ab

(X+1)^2 - (y-1)^2

= X^2 + 1 + 2x - ( y^2 + 1 -2y)
= X^2 + 1 + 2x - y^2 - 1 + 2y
= X^2 -y^2 +2x + 2y
= (X+y) ( x -y) + 2(x+y)
= (X+y) {(x-y) + 2}

Hope it helps you!

Answer 2

(x + 1)^2=X^2 + 2x +1
(y-1)^2=y^2 -2y+1
(x+1)^2 - (y-1)^2=X^2 + 2x +1-(y^2 -2y+1)
=X^2 + 2x +1-y^2 +2y-1
=X^2-y^2 + 2x +2y