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a2-b2 type expressions

3.  a^{2}- b^{2}  type expressions

 a^{2}- b^{2} is product of (a-b)(a+b) factors. To factorize such type expressions, we convert a given expression into  a^{2}- b^{2} form and then factorize it by writing it in (a-b)(a+b) form. See example below;

Example: Factorize 6x ^{4}-96

Solution:

To factorize this expression we first apply type 1 technique i-e take out anything common. Here 6 is common – which we take out;

i-e

6x ^{4}-96

=6(x ^{4}-16)

Then we convert expression inside brackets to  a^{2}-b ^{2} form;

i-e

 = 6[(x^{2})^{2}-(4)^{2}]

And then factorize it in (a-b)(a+b) form;

 = 6[(x^{2}-4)(x^{2}+4)]

Again we can see that  (x^{2}-4) can be converted to (a-b)(a+b) form – so above expression will become;

=6[(x^{2}-2^{2})(x^{2}+4)]

Again apply (a-b)(a+b) form here;

=6[(x-2)(x+2)(x^{2}+4)]

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