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

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

Evaluate

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

Solution Steps

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

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

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

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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

Expand

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

Solution Steps

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

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

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

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

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$x^{8}-\left(y^{4}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

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