a 2 ± 2ab + b 2 type expressions

4.       a^{2}\pm2ab+ b^{2}   type expressions

When we multiply a number say 3 with itself i-e 3×3 then we get 9 or  3^{2}

If we multiply (a+b) with itself i-e (a+b)(a+b) then we will get  a^{2}+2ab+ b^{2}  or  (a+b)^{2}

Similarly if we multiply (a-b) with itself i-e (a-b)(a-b) then we will get  a^{2}-2ab+ b^{2}   or (a-b)^{2}

So, we can say that (a+b) is two time factor of  a^{2}+2ab+ b^{2}

and (a-b) is two time factor of   a^{2}-2ab+ b^{2}

Hence to factorize such expressions we try to make them a whole square of some algebric expression and in this way we get it two time factor and factorization is complete.

Example: Factorize  25x^{2}+16+40x 

Solution: 

To factorize this expression we try to make whole square of it

i-e

 25x^{2}+16+40x

=25x^{2}+40x+16

= (5x)^{2}+(5x)(4)+ (4)^{2}

= (5x+4)^{2}

 

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