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

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

Evaluate

$$3x^{2}-8x+7$$

Solution Steps

Use the distributive property to multiply x^{2}-3 by x+1.

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

Use the distributive property to multiply x^{2}+5 by x-2.

$$x^{3}+x^{2}-3x-3-\left(x^{3}-2x^{2}+5x-10\right)$$

To find the opposite of x^{3}-2x^{2}+5x-10, find the opposite of each term.

$$x^{3}+x^{2}-3x-3-x^{3}+2x^{2}-5x+10$$

Combine x^{3} and -x^{3} to get 0.

$$x^{2}-3x-3+2x^{2}-5x+10$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}-3x-3-5x+10$$

Combine -3x and -5x to get -8x.

$$3x^{2}-8x-3+10$$

Add -3 and 10 to get 7.

$$3x^{2}-8x+7$$

Expand

$$3x^{2}-8x+7$$

Solution Steps

Use the distributive property to multiply x^{2}-3 by x+1.

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

Use the distributive property to multiply x^{2}+5 by x-2.

$$x^{3}+x^{2}-3x-3-\left(x^{3}-2x^{2}+5x-10\right)$$

To find the opposite of x^{3}-2x^{2}+5x-10, find the opposite of each term.

$$x^{3}+x^{2}-3x-3-x^{3}+2x^{2}-5x+10$$

Combine x^{3} and -x^{3} to get 0.

$$x^{2}-3x-3+2x^{2}-5x+10$$

Combine x^{2} and 2x^{2} to get 3x^{2}.

$$3x^{2}-3x-3-5x+10$$

Combine -3x and -5x to get -8x.

$$3x^{2}-8x-3+10$$

Add -3 and 10 to get 7.

$$3x^{2}-8x+7$$