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

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

Evaluate

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

Solution Steps

Use the distributive property to multiply x-y by x+y and combine like terms.

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

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

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

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

$$x^{6}-y^{6}$$

Expand

$$x^{6}-y^{6}$$

Solution Steps

Use the distributive property to multiply x-y by x+y and combine like terms.

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

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

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

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

$$x^{6}-y^{6}$$