Solve (x^5-x^4-2x^3-3x^2-4x-5)(2{x}^2+5x+13)+32{x}^4+79{x}^3+189{x}^2+262x+246

$$( { x }^{ 5 } - { x }^{ 4 } -2 { x }^{ 3 } -3 { x }^{ 2 } -4x-5)(2 { x }^{ 2 } +5x+13)+32 { x }^{ 4 } +79 { x }^{ 3 } +189 { x }^{ 2 } +262x+246$$

Evaluate

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x+181$$

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.

$$2x^{7}+3x^{6}+4x^{5}-29x^{4}-49x^{3}-69x^{2}-77x-65+32x^{4}+79x^{3}+189x^{2}+262x+246$$

Combine -29x^{4} and 32x^{4} to get 3x^{4}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}-49x^{3}-69x^{2}-77x-65+79x^{3}+189x^{2}+262x+246$$

Combine -49x^{3} and 79x^{3} to get 30x^{3}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}-69x^{2}-77x-65+189x^{2}+262x+246$$

Combine -69x^{2} and 189x^{2} to get 120x^{2}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}-77x-65+262x+246$$

Combine -77x and 262x to get 185x.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x-65+246$$

Add -65 and 246 to get 181.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x+181$$

Expand

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x+181$$

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.

$$2x^{7}+3x^{6}+4x^{5}-29x^{4}-49x^{3}-69x^{2}-77x-65+32x^{4}+79x^{3}+189x^{2}+262x+246$$

Combine -29x^{4} and 32x^{4} to get 3x^{4}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}-49x^{3}-69x^{2}-77x-65+79x^{3}+189x^{2}+262x+246$$

Combine -49x^{3} and 79x^{3} to get 30x^{3}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}-69x^{2}-77x-65+189x^{2}+262x+246$$

Combine -69x^{2} and 189x^{2} to get 120x^{2}.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}-77x-65+262x+246$$

Combine -77x and 262x to get 185x.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x-65+246$$

Add -65 and 246 to get 181.

$$2x^{7}+3x^{6}+4x^{5}+3x^{4}+30x^{3}+120x^{2}+185x+181$$