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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