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

5. a 2 + 2ab + b 2 – c 2 type expressions

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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