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

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

Evaluate

$$9-5x-14x^{2}-2x^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

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

$$-2x^{3}-8x^{2}-8x-3\left(x+1\right)\left(2x-3\right)$$

Use the distributive property to multiply -3 by x+1.

$$-2x^{3}-8x^{2}-8x+\left(-3x-3\right)\left(2x-3\right)$$

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

$$-2x^{3}-8x^{2}-8x-6x^{2}+3x+9$$

Combine -8x^{2} and -6x^{2} to get -14x^{2}.

$$-2x^{3}-14x^{2}-8x+3x+9$$

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

$$-2x^{3}-14x^{2}-5x+9$$

Expand

$$9-5x-14x^{2}-2x^{3}$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+2\right)^{2}.

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

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

$$-2x^{3}-8x^{2}-8x-3\left(x+1\right)\left(2x-3\right)$$

Use the distributive property to multiply -3 by x+1.

$$-2x^{3}-8x^{2}-8x+\left(-3x-3\right)\left(2x-3\right)$$

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

$$-2x^{3}-8x^{2}-8x-6x^{2}+3x+9$$

Combine -8x^{2} and -6x^{2} to get -14x^{2}.

$$-2x^{3}-14x^{2}-8x+3x+9$$

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

$$-2x^{3}-14x^{2}-5x+9$$