a 2 ± 2ab + b 2 type expressions

4. a 2 ± 2ab + b 2 type expressions 0

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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a 2 ± 2ab + b 2 type expressions

You may submit a MCQ or maths problem with solution tips here in the comment box below! If you could not solve anyone, you may submit a MCQ or maths problem without solution as well. We will try our level best to solve it for you! Cancel Reply

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