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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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