Solve f(x)=2(x+2)(x-5)(x+4)

$$f ( x ) = 2 ( x + 2 ) ( x - 5 ) ( x + 4 )$$

Evaluate

$$2\left(x-5\right)\left(x+2\right)\left(x+4\right)$$

Solution Steps

Use the distributive property to multiply 2 by x+2.

$$\left(2x+4\right)\left(x-5\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-5.

$$\left(2x^{2}-10x+4x-20\right)\left(x+4\right)$$

Combine -10x and 4x to get -6x.

$$\left(2x^{2}-6x-20\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x^{2}-6x-20 by each term of x+4.

$$2x^{3}+8x^{2}-6x^{2}-24x-20x-80$$

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

$$2x^{3}+2x^{2}-24x-20x-80$$

Combine -24x and -20x to get -44x.

$$2x^{3}+2x^{2}-44x-80$$

Expand

$$2x^{3}+2x^{2}-44x-80$$

Solution Steps

Use the distributive property to multiply 2 by x+2.

$$\left(2x+4\right)\left(x-5\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x+4 by each term of x-5.

$$\left(2x^{2}-10x+4x-20\right)\left(x+4\right)$$

Combine -10x and 4x to get -6x.

$$\left(2x^{2}-6x-20\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x^{2}-6x-20 by each term of x+4.

$$2x^{3}+8x^{2}-6x^{2}-24x-20x-80$$

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

$$2x^{3}+2x^{2}-24x-20x-80$$

Combine -24x and -20x to get -44x.

$$2x^{3}+2x^{2}-44x-80$$