Question

(x-y)2 – (a-b)2 factorize

Answer 1

The factorisation of $(x-y)^2-(a-b)^2$ is equal to (x - y + a - b)(x - y - a + b).

Step-by-step explanation:

We have,

$(x-y)^2-(a-b)^2$

To find, the factorisation of $(x-y)^2-(a-b)^2$ = ?

∴ $(x-y)^2-(a-b)^2$

Using the algebraic identity,

$A^{2}-B^{2}=(A+B)(A-B)$

Here, A = x - y and B = a - b

= (A +  B)(A - B)

= [(x - y) + (a - b)][(x - y) - (a - b)]

= (x - y + a - b)(x - y - a + b)

∴ The factorisation of $(x-y)^2-(a-b)^2$ = (x - y + a - b)(x - y - a + b)

Thus, the factorisation of $(x-y)^2-(a-b)^2$ is equal to (x - y + a - b)(x - y - a + b).