Solve left(left(x+x^2+x^3right)left(x-x^2-x^3right)+{x}^6right)2{x}^2

$$\left( \left( x+ { x }^{ 2 } + { x }^{ 3 } \right) \left( x- { x }^{ 2 } - { x }^{ 3 } \right) + { x }^{ 6 } \right) 2 { x }^{ 2 }$$

Evaluate

$$-2\left(2x^{3}+x^{2}-1\right)x^{4}$$

Solution Steps

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

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

Combine -x^{6} and x^{6} to get 0.

$$\left(x^{2}-x^{4}-2x^{5}\right)\times 2x^{2}$$

Use the distributive property to multiply x^{2}-x^{4}-2x^{5} by 2.

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

Use the distributive property to multiply 2x^{2}-2x^{4}-4x^{5} by x^{2}.

$$2x^{4}-2x^{6}-4x^{7}$$

Expand

$$2x^{4}-2x^{6}-4x^{7}$$

Solution Steps

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

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

Combine -x^{6} and x^{6} to get 0.

$$\left(x^{2}-x^{4}-2x^{5}\right)\times 2x^{2}$$

Use the distributive property to multiply x^{2}-x^{4}-2x^{5} by 2.

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

Use the distributive property to multiply 2x^{2}-2x^{4}-4x^{5} by x^{2}.

$$2x^{4}-2x^{6}-4x^{7}$$