$ \mathrm{a}^{2}-\mathrm{b}^{2} $ is a product of ____ and ____.

Given :   

$ \ ( \mathrm{a}^{2}-\mathrm{b}^{2}  \ ) $

Solution : 

$$\displaystyle a^{2} \ -\ b^{2} \ \ \ is\ the\ product\ of\ \ ( a+b) \ \ ( a-b) \ $$

Multiply 'a' and 'a'    $$\displaystyle a\ \times \ a\ =\ a^{2}$$

Multiply 'a' and '-b'   $$\displaystyle a\ \times \ -b\ =\ -\ ab$$

Multiply 'b' and 'a'   $$\displaystyle a\ \times \ b\ =\ \ ab$$

Multiply 'b' and '-b'    $$\displaystyle b\ \times \ -b\ =\ \ -b\ ^{2}$$

Add all the terms,

$$\displaystyle \ \ ( a+b) \ \ ( a-b) \ \ =\ \ a^{2} \ +\ ab\ -\ ab\ -\ b^{2} \ $$

$ab - ab  =  0$

$$\displaystyle \ \ ( a+b) \ \ ( a-b) \ \ =\ \ a^{2} \ \ -\ b^{2} \ $$

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Updated on: 10-Oct-2022

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