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Factroize (i) x^2-1-2a-a^2 (ii) 1+2a...

Factroize
`(i) x^2-1-2a-a^2`
`(ii) 1+2ab-(a^2+b^2)`

Text Solution

Verified by Experts

We have
`(i) x^2-1-2a-a^2`
` =x^2-(1+2a+a^2)`
`=x^2-(1+a)^2`
`{x-(1+a)}{x+(1+a)}`
`=(x-1-a)(x+1+a)`.
`therefore (x^2-1-2a-a^2)=(x-1-a)(x+1+a)`.
`(ii) 1+2ab-(a^2+b^2)`
` =1-(a^2+b^2-2ab)`
` =1^2-(a-b)^2`
`={1-(a-b)}{(1+(a-b)}`
`(1-a+b)(1+a-b)`.
`therefore 1+2ab-(a^2+b^2)=(1-a+b)(1+a-b)`.
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