Mathematics
Factorize:
x2 - 4x + 4y - y2
Factorisation
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Answer
Given,
⇒ x2 - 4x + 4y - y2
⇒ (x2 - 4x) - (y2 - 4y)
⇒ (x2 - 4x) + 4 - 4 - (y2 - 4y)
⇒ (x2 - 4x + 4) - (y2 - 4y + 4)
⇒ (x - 2)2 - (y - 2)2
⇒ (x - 2 + y - 2)[x - 2 - (y - 2)]
⇒ (x - 2 + y - 2)(x - 2 - y + 2)
⇒ (x + y - 4)(x - y).
Hence, x2 - 4x + 4y - y2 = (x - y)(x + y - 4).
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