Solve (4)(x^2-3)*(x+1)-(x^2+5)*(x-2)

$$( 4 ) ( x ^ { 2 } - 3 ) \cdot ( x + 1 ) - ( x ^ { 2 } + 5 ) \cdot ( x - 2 )$$

Evaluate

$$3x^{3}+6x^{2}-17x-2$$

Solution Steps

Use the distributive property to multiply 4 by x^{2}-3.

$$\left(4x^{2}-12\right)\left(x+1\right)-\left(x^{2}+5\right)\left(x-2\right)$$

Use the distributive property to multiply 4x^{2}-12 by x+1.

$$4x^{3}+4x^{2}-12x-12-\left(x^{2}+5\right)\left(x-2\right)$$

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

$$4x^{3}+4x^{2}-12x-12-\left(x^{3}-2x^{2}+5x-10\right)$$

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

$$4x^{3}+4x^{2}-12x-12-x^{3}+2x^{2}-5x+10$$

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

$$3x^{3}+4x^{2}-12x-12+2x^{2}-5x+10$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$3x^{3}+6x^{2}-12x-12-5x+10$$

Combine -12x and -5x to get -17x.

$$3x^{3}+6x^{2}-17x-12+10$$

Add -12 and 10 to get -2.

$$3x^{3}+6x^{2}-17x-2$$

Expand

$$3x^{3}+6x^{2}-17x-2$$

Solution Steps

Use the distributive property to multiply 4 by x^{2}-3.

$$\left(4x^{2}-12\right)\left(x+1\right)-\left(x^{2}+5\right)\left(x-2\right)$$

Use the distributive property to multiply 4x^{2}-12 by x+1.

$$4x^{3}+4x^{2}-12x-12-\left(x^{2}+5\right)\left(x-2\right)$$

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

$$4x^{3}+4x^{2}-12x-12-\left(x^{3}-2x^{2}+5x-10\right)$$

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

$$4x^{3}+4x^{2}-12x-12-x^{3}+2x^{2}-5x+10$$

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

$$3x^{3}+4x^{2}-12x-12+2x^{2}-5x+10$$

Combine 4x^{2} and 2x^{2} to get 6x^{2}.

$$3x^{3}+6x^{2}-12x-12-5x+10$$

Combine -12x and -5x to get -17x.

$$3x^{3}+6x^{2}-17x-12+10$$

Add -12 and 10 to get -2.

$$3x^{3}+6x^{2}-17x-2$$