d Factorize x 2 − y 2 − 6y − 9 How to factorize ? Any way?

Question 5 : Factorize x 2 − y 2 − 6y − 9

Question 5: Factorize  x^{2}- y^{2}-6y-9

How to factorize ?


This is a problem of factorization in which two type of factoring is applicable We first reform the expression’s one part to be a whole square and then finally get x2-y2 form to factorize.

Given expression is

 x^{2}- y^{2}-6y-9

First we reform last three terms to whole square format. For this we take minus sign out from the terms – making inner bracket terms positive!

so, we get  =x^{2}- (y^{2}+6y+9)

We brake mid term in the bracket in two terms like that on left and right- and form it like a2+2ab+b2 from.

so,  =x^{2}- [ (y)^{2}+2(3)(y)+ (3)^{2})]

We see that the terms in side bracket are now whole square of y+1

hence, = (x)^{2} - (y+1)^{2}

now we apply x2-y2 formula to factorize !


hence finally = [x+y+1][x-y-1]

This the factorization !



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