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Question

Divide: $$\left( { x }^{ 4 }-{ y }^{ 4 } \right) $$ by $$\left( x-y \right) $$. Is $$\left( x-y \right) $$ a factor of $$\left( { x }^{ 4 }-{ y }^{ 4 } \right) $$?


Solution

As we know that $$x^2-y^2 = (x+y)(x-y)$$

Then using this formula we simplify this expression as:

 $$x^4-y^4 = (x^2)^2-(y^2)^2 = (x^2+y^2)(x^2-y^2) = (x^2+y^2)(x+y)(x-y) $$

Then dividing the expression by x-y we have:

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

Hence, it a factor of $$x^4-y^4$$


Mathematics

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