Question 2: Factorize x 2 − y 2 − 4 x − 2y + 3

Question 2: Factorize   x^{2}- y^{2} -4x-2y+3

How to factorize ?

Solution:

Given expression is

 x^{2}- y^{2} -4x-2y+3

To convert it to a factorize-able form ,  we add 1 and subtract 1, so that expression remains same ;

= x^{2}- y^{2} -4x-2y+3 +1 -1

 =x^{2}- y^{2} -4x-2y+4 -1

Rearranging terms as below;

 =x^{2}-4x+4- y^{2} -2y -1

 =x^{2}-4x+4- (y^{2} +2y+1)

 =[(x+2)^{2}-(y+1)^{2}]}

Now this is in  a^{2}-b ^{2}=(a+b)(a-b) form !

Where;

(x+2) stands for a

and

(y+1) stands for b

So, according to formula;

 =[(x+2)+(y+1)][(x+2)-(y+1)]

 =[x+2+y+1][x+2-y+1]

 =[x+y+3][x-y+3]

 

 


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