d Factorize x 2 − y 2 − 4 x z + 4z 2 How to factorize ?
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Question 4: Factorize x 2 − y 2 − 4 x z + 4z 2

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

 

How to factorize ?

Solution:

 

To factorize this expression we first re-arrange terms as below

 x^{2}- y^{2}-4xz+4 z^{2}

so, we get ,  =x^{2}-4xz+4 z^{2}- y^{2}

Now brake second term as product of 2x and 2z as below

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

Now first three terms are whole square expansion of  (x+2y) as you see below!

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

This is now a2-b2 form expression where a= x+2z-y and b= x+2z+y, so we get

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

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