Question

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



please solve this problem I will give you brilliant ​

Answer 1

The factorisation of (x-y)^2-(a-b)^2(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(x−y)

2

−(a−b)

2

To find, the factorisation of (x-y)^2-(a-b)^2(x−y)

2

−(a−b)

2

= ?

∴ (x-y)^2-(a-b)^2(x−y)

2

−(a−b)

2

Using the algebraic identity,

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

2

−(a−b)

2

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

Thus, the factorisation of (x-y)^2-(a-b)^2(x−y)

2

−(a−b)

2

is equal to (x - y + a - b)(x - y - a + b).