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Factorize a(a-1)-b(b-1)....

Factorize `a(a-1)-b(b-1)`.

Text Solution

Verified by Experts

We have
`a(a-1)-b(b-a) =a^1-a-b^2+b`
`=(a^2-b^2)-(a-b)`
`=(a-b)(a+b)-(a-b)`
`=(a-b){(a+b)-1}`
`=(a-b)(a+b-1)`.
Hence, `a(a-1)-b(b-1)=(a-b)(a+b-1)`.
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