Solve left(2x^4+5x^3+13x^2+34x^+89right)left({x}^{5}-{x}^{4}-2{x}^{3}-3{x}^2-4x-5right)+233{x}^4+365{x}^3+477{x}^2+536x+456

$$\left( 2 { x }^{ 4 } +5 { x }^{ 3 } +13 { x }^{ 2 } +34 { x }^{ } +89 \right) \left( { x }^{ 5 } - { x }^{ 4 } -2 { x }^{ 3 } -3 { x }^{ 2 } -4x-5 \right) +233 { x }^{ 4 } +365 { x }^{ 3 } +477 { x }^{ 2 } +536x+456$$

Evaluate

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x+11$$

Solution Steps

Calculate x to the power of 1 and get x.

$$\left(2x^{4}+5x^{3}+13x^{2}+34x+89\right)\left(x^{5}-x^{4}-2x^{3}-3x^{2}-4x-5\right)+233x^{4}+365x^{3}+477x^{2}+536x+456$$

Use the distributive property to multiply 2x^{4}+5x^{3}+13x^{2}+34x+89 by x^{5}-x^{4}-2x^{3}-3x^{2}-4x-5 and combine like terms.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}-226x^{4}-357x^{3}-468x^{2}-526x-445+233x^{4}+365x^{3}+477x^{2}+536x+456$$

Combine -226x^{4} and 233x^{4} to get 7x^{4}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}-357x^{3}-468x^{2}-526x-445+365x^{3}+477x^{2}+536x+456$$

Combine -357x^{3} and 365x^{3} to get 8x^{3}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}-468x^{2}-526x-445+477x^{2}+536x+456$$

Combine -468x^{2} and 477x^{2} to get 9x^{2}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}-526x-445+536x+456$$

Combine -526x and 536x to get 10x.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x-445+456$$

Add -445 and 456 to get 11.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x+11$$

Expand

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x+11$$

Solution Steps

Calculate x to the power of 1 and get x.

$$\left(2x^{4}+5x^{3}+13x^{2}+34x+89\right)\left(x^{5}-x^{4}-2x^{3}-3x^{2}-4x-5\right)+233x^{4}+365x^{3}+477x^{2}+536x+456$$

Use the distributive property to multiply 2x^{4}+5x^{3}+13x^{2}+34x+89 by x^{5}-x^{4}-2x^{3}-3x^{2}-4x-5 and combine like terms.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}-226x^{4}-357x^{3}-468x^{2}-526x-445+233x^{4}+365x^{3}+477x^{2}+536x+456$$

Combine -226x^{4} and 233x^{4} to get 7x^{4}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}-357x^{3}-468x^{2}-526x-445+365x^{3}+477x^{2}+536x+456$$

Combine -357x^{3} and 365x^{3} to get 8x^{3}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}-468x^{2}-526x-445+477x^{2}+536x+456$$

Combine -468x^{2} and 477x^{2} to get 9x^{2}.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}-526x-445+536x+456$$

Combine -526x and 536x to get 10x.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x-445+456$$

Add -445 and 456 to get 11.

$$2x^{9}+3x^{8}+4x^{7}+5x^{6}+6x^{5}+7x^{4}+8x^{3}+9x^{2}+10x+11$$