Solve (x^2-9)*(x^2+8)-(x^2-5)*(x^2+3x-2)=

$$( x ^ { 2 } - 9 ) \cdot ( x ^ { 2 } + 8 ) - ( x ^ { 2 } - 5 ) \cdot ( x ^ { 2 } + 3 x - 2 ) =$$

Evaluate

$$-3x^{3}+6x^{2}+15x-82$$

Solution Steps

Use the distributive property to multiply x^{2}-9 by x^{2}+8 and combine like terms.

$$x^{4}-x^{2}-72-\left(x^{2}-5\right)\left(x^{2}+3x-2\right)$$

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

$$x^{4}-x^{2}-72-\left(x^{4}+3x^{3}-7x^{2}-15x+10\right)$$

To find the opposite of x^{4}+3x^{3}-7x^{2}-15x+10, find the opposite of each term.

$$x^{4}-x^{2}-72-x^{4}-3x^{3}+7x^{2}+15x-10$$

Combine x^{4} and -x^{4} to get 0.

$$-x^{2}-72-3x^{3}+7x^{2}+15x-10$$

Combine -x^{2} and 7x^{2} to get 6x^{2}.

$$6x^{2}-72-3x^{3}+15x-10$$

Subtract 10 from -72 to get -82.

$$6x^{2}-82-3x^{3}+15x$$

Expand

$$-3x^{3}+6x^{2}+15x-82$$

Solution Steps

Use the distributive property to multiply x^{2}-9 by x^{2}+8 and combine like terms.

$$x^{4}-x^{2}-72-\left(x^{2}-5\right)\left(x^{2}+3x-2\right)$$

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

$$x^{4}-x^{2}-72-\left(x^{4}+3x^{3}-7x^{2}-15x+10\right)$$

To find the opposite of x^{4}+3x^{3}-7x^{2}-15x+10, find the opposite of each term.

$$x^{4}-x^{2}-72-x^{4}-3x^{3}+7x^{2}+15x-10$$

Combine x^{4} and -x^{4} to get 0.

$$-x^{2}-72-3x^{3}+7x^{2}+15x-10$$

Combine -x^{2} and 7x^{2} to get 6x^{2}.

$$6x^{2}-72-3x^{3}+15x-10$$

Subtract 10 from -72 to get -82.

$$6x^{2}-82-3x^{3}+15x$$