Solve left(x-2yright)^left(x^2+4y^2right)left(x+2yright)

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

Evaluate

$$x^{4}-16y^{4}$$

Solution Steps

Calculate x-2y to the power of 1 and get x-2y.

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

Use the distributive property to multiply x-2y by x^{2}+4y^{2}.

$$\left(x^{3}+4xy^{2}-2yx^{2}-8y^{3}\right)\left(x+2y\right)$$

Use the distributive property to multiply x^{3}+4xy^{2}-2yx^{2}-8y^{3} by x+2y and combine like terms.

$$x^{4}-16y^{4}$$

Expand

$$x^{4}-16y^{4}$$

Solution Steps

Calculate x-2y to the power of 1 and get x-2y.

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

Use the distributive property to multiply x-2y by x^{2}+4y^{2}.

$$\left(x^{3}+4xy^{2}-2yx^{2}-8y^{3}\right)\left(x+2y\right)$$

Use the distributive property to multiply x^{3}+4xy^{2}-2yx^{2}-8y^{3} by x+2y and combine like terms.

$$x^{4}-16y^{4}$$