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