Question

Find the factors of x^5y-xy^5

Answer 1

Answer:

x^5y-xy^5

Taking x and y common ;

xy {x^4 - y^4}

xy {(x^2)^2 - (y^2)^2}

Now it is in the form of a^2 - b^2....

By the identity a^2 - b^2 = (a+b)(a-b)...

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

→ xy{x^2+y^2}{x+y}{x-y}

The ans. is

xy(x^2+y^2)(x+y)(x-y)

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