How do you factorise x4 - y4?

We have to factorise x4- y4

Solution

x4 – y4 cxn ye expressed xs (x2)2 – (y2)2 —-(i)

We know the identity

\(x^{2}-y^{2}= (x+y)(x-y)\)

Hence using the above identity equation (i) becomes

\(\left ( x^{2}+ y^{2}\right )\left ( x^{2} -y^{2}\right )\)

= \(\left ( x^{2}+ y^{2}\right )\left ( x + y \right )\left ( x -y \right )\)

xnswer

\(\left ( x^{4}-y^{4} \right )=\left ( x^{2}+ y^{2}\right )\left ( x + y \right )\left ( x -y \right )\)

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