Solve (x+1)(x-2)(x+3)(x-5)+x^2-1

$$(x+1)(x-2)(x+3)(x-5)+ { x }^{ 2 } -1$$

Evaluate

$$\left(x+1\right)\left(x^{3}-4x^{2}-10x+29\right)$$

Solution Steps

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$\left(x^{2}-x-2\right)\left(x+3\right)\left(x-5\right)+x^{2}-1$$

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

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-5\right)+x^{2}-1$$

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

$$x^{4}-3x^{3}-15x^{2}+19x+30+x^{2}-1$$

Combine -15x^{2} and x^{2} to get -14x^{2}.

$$x^{4}-3x^{3}-14x^{2}+19x+30-1$$

Subtract 1 from 30 to get 29.

$$x^{4}-3x^{3}-14x^{2}+19x+29$$

Expand

$$x^{4}-3x^{3}-14x^{2}+19x+29$$

Solution Steps

Use the distributive property to multiply x+1 by x-2 and combine like terms.

$$\left(x^{2}-x-2\right)\left(x+3\right)\left(x-5\right)+x^{2}-1$$

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

$$\left(x^{3}+2x^{2}-5x-6\right)\left(x-5\right)+x^{2}-1$$

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

$$x^{4}-3x^{3}-15x^{2}+19x+30+x^{2}-1$$

Combine -15x^{2} and x^{2} to get -14x^{2}.

$$x^{4}-3x^{3}-14x^{2}+19x+30-1$$

Subtract 1 from 30 to get 29.

$$x^{4}-3x^{3}-14x^{2}+19x+29$$