Factorise a4 - b4

We have to factorise a4- b4

Solution

a4 – b4 can be expressed as (a2)2 – (b2)2 —-(i)

We know the identity

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

Hence using the above identityequation (i) becomes

\(\left ( a^{2}+ b^{2}\right )\left ( a^{2} -b^{2}\right )\)

= \(\left ( a^{2}+ b^{2}\right )\left ( a + b \right )\left ( a -b \right )\)

Answer

\(\left ( a^{4}-b^{4} \right )=\left ( a^{2}+ b^{2}\right )\left ( a + b \right )\left ( a -b \right )\)

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