Solve (x^4+y^4)(x^2+y^2)(x+y)(x-y)

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

Evaluate

$$x^{8}-y^{8}$$

Solution Steps

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

$$\left(x^{6}+x^{4}y^{2}+y^{4}x^{2}+y^{6}\right)\left(x+y\right)\left(x-y\right)$$

Use the distributive property to multiply x^{6}+x^{4}y^{2}+y^{4}x^{2}+y^{6} by x+y.

$$\left(x^{7}+x^{6}y+y^{2}x^{5}+x^{4}y^{3}+y^{4}x^{3}+x^{2}y^{5}+y^{6}x+y^{7}\right)\left(x-y\right)$$

Use the distributive property to multiply x^{7}+x^{6}y+y^{2}x^{5}+x^{4}y^{3}+y^{4}x^{3}+x^{2}y^{5}+y^{6}x+y^{7} by x-y and combine like terms.

$$x^{8}-y^{8}$$

Expand

$$x^{8}-y^{8}$$

Solution Steps

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

$$\left(x^{6}+x^{4}y^{2}+y^{4}x^{2}+y^{6}\right)\left(x+y\right)\left(x-y\right)$$

Use the distributive property to multiply x^{6}+x^{4}y^{2}+y^{4}x^{2}+y^{6} by x+y.

$$\left(x^{7}+x^{6}y+y^{2}x^{5}+x^{4}y^{3}+y^{4}x^{3}+x^{2}y^{5}+y^{6}x+y^{7}\right)\left(x-y\right)$$

Use the distributive property to multiply x^{7}+x^{6}y+y^{2}x^{5}+x^{4}y^{3}+y^{4}x^{3}+x^{2}y^{5}+y^{6}x+y^{7} by x-y and combine like terms.

$$x^{8}-y^{8}$$