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

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

Evaluate

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

Solution Steps

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

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

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

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

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

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

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

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

Expand

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

Solution Steps

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

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

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

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

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

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

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

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