Solve (x - y)(x + y)(x ^ 2 + y ^ 2)(x ^ 4 + y ^ 4) a ) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Evaluate

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

Solution Steps

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

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

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

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

Use the distributive property to multiply $x^{2}-y^{2}$ by $x^{2}+y^{2}$ 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 $8$.

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