Solve (2-x-x^6)(2-x^2-x^5)(2-x^3-{x}^4)

$$(2-x- { x }^{ 6 } )(2- { x }^{ 2 } - { x }^{ 5 } )(2- { x }^{ 3 } - { x }^{ 4 } )$$

Evaluate

$$\left(2-x^{3}-x^{4}\right)\left(2-x^{2}-x^{5}\right)\left(2-x-x^{6}\right)$$

Solution Steps

Use the distributive property to multiply 2-x-x^{6} by 2-x^{2}-x^{5} and combine like terms.

$$\left(4-2x^{2}-2x^{5}-2x+x^{3}-x^{6}+x^{8}+x^{11}\right)\left(2-x^{3}-x^{4}\right)$$

Use the distributive property to multiply 4-2x^{2}-2x^{5}-2x+x^{3}-x^{6}+x^{8}+x^{11} by 2-x^{3}-x^{4} and combine like terms.

$$8-2x^{3}-2x^{4}-4x^{2}-x^{6}+4x^{8}+3x^{9}-4x-x^{7}+x^{10}+x^{11}-x^{12}-x^{14}-x^{15}$$

Expand

$$8-4x-4x^{2}-2x^{3}-2x^{4}-x^{6}-x^{7}+4x^{8}+3x^{9}+x^{10}+x^{11}-x^{12}-x^{14}-x^{15}$$

Solution Steps

Use the distributive property to multiply 2-x-x^{6} by 2-x^{2}-x^{5} and combine like terms.

$$\left(4-2x^{2}-2x^{5}-2x+x^{3}-x^{6}+x^{8}+x^{11}\right)\left(2-x^{3}-x^{4}\right)$$

Use the distributive property to multiply 4-2x^{2}-2x^{5}-2x+x^{3}-x^{6}+x^{8}+x^{11} by 2-x^{3}-x^{4} and combine like terms.

$$8-2x^{3}-2x^{4}-4x^{2}-x^{6}+4x^{8}+3x^{9}-4x-x^{7}+x^{10}+x^{11}-x^{12}-x^{14}-x^{15}$$