Solve (x^5-x^4-2x^3-3x^2-4x-5)(2{x}^2+5x+13)+35{x}^4+54{x}^3+76{x}^2+85x+74

$$( { x }^{ 5 } - { x }^{ 4 } -2 { x }^{ 3 } -3 { x }^{ 2 } -4x-5)(2 { x }^{ 2 } +5x+13)+35 { x }^{ 4 } +54 { x }^{ 3 } +76 { x }^{ 2 } +85x+74$$

Evaluate

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

Solution Steps

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

$$2x^{7}+3x^{6}+4x^{5}-29x^{4}-49x^{3}-69x^{2}-77x-65+35x^{4}+54x^{3}+76x^{2}+85x+74$$

Combine -29x^{4} and 35x^{4} to get 6x^{4}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}-49x^{3}-69x^{2}-77x-65+54x^{3}+76x^{2}+85x+74$$

Combine -49x^{3} and 54x^{3} to get 5x^{3}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}-69x^{2}-77x-65+76x^{2}+85x+74$$

Combine -69x^{2} and 76x^{2} to get 7x^{2}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}+7x^{2}-77x-65+85x+74$$

Combine -77x and 85x to get 8x.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}+7x^{2}+8x-65+74$$

Add -65 and 74 to get 9.

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

Expand

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

Solution Steps

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

$$2x^{7}+3x^{6}+4x^{5}-29x^{4}-49x^{3}-69x^{2}-77x-65+35x^{4}+54x^{3}+76x^{2}+85x+74$$

Combine -29x^{4} and 35x^{4} to get 6x^{4}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}-49x^{3}-69x^{2}-77x-65+54x^{3}+76x^{2}+85x+74$$

Combine -49x^{3} and 54x^{3} to get 5x^{3}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}-69x^{2}-77x-65+76x^{2}+85x+74$$

Combine -69x^{2} and 76x^{2} to get 7x^{2}.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}+7x^{2}-77x-65+85x+74$$

Combine -77x and 85x to get 8x.

$$2x^{7}+3x^{6}+4x^{5}+6x^{4}+5x^{3}+7x^{2}+8x-65+74$$

Add -65 and 74 to get 9.

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