Solve (x-2)(16+x^4)(2+x)(4+x^2)

$$( x - 2 ) ( 16 + x ^ { 4 } ) ( 2 + x ) ( 4 + x ^ { 2 } )$$

Evaluate

$$x^{8}-256$$

Solution Steps

Use the distributive property to multiply x-2 by 16+x^{4}.

$$\left(16x+x^{5}-32-2x^{4}\right)\left(2+x\right)\left(4+x^{2}\right)$$

Use the distributive property to multiply 16x+x^{5}-32-2x^{4} by 2+x and combine like terms.

$$\left(16x^{2}+x^{6}-64-4x^{4}\right)\left(4+x^{2}\right)$$

Use the distributive property to multiply 16x^{2}+x^{6}-64-4x^{4} by 4+x^{2} and combine like terms.

$$x^{8}-256$$

Expand

$$x^{8}-256$$

Solution Steps

Use the distributive property to multiply x-2 by 16+x^{4}.

$$\left(16x+x^{5}-32-2x^{4}\right)\left(2+x\right)\left(4+x^{2}\right)$$

Use the distributive property to multiply 16x+x^{5}-32-2x^{4} by 2+x and combine like terms.

$$\left(16x^{2}+x^{6}-64-4x^{4}\right)\left(4+x^{2}\right)$$

Use the distributive property to multiply 16x^{2}+x^{6}-64-4x^{4} by 4+x^{2} and combine like terms.

$$x^{8}-256$$