Solve +(x+2)(x+3)(4-x)

$$+ ( x + 2 ) ( x + 3 ) ( 4 - x )$$

Evaluate

$$\left(4-x\right)\left(x+2\right)\left(x+3\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x+3.

$$\left(x^{2}+3x+2x+6\right)\left(4-x\right)$$

Combine 3x and 2x to get 5x.

$$\left(x^{2}+5x+6\right)\left(4-x\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of 4-x.

$$4x^{2}-x^{3}+20x-5x^{2}+24-6x$$

Combine 4x^{2} and -5x^{2} to get -x^{2}.

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

Combine 20x and -6x to get 14x.

$$-x^{2}-x^{3}+14x+24$$

Expand

$$24+14x-x^{2}-x^{3}$$

Solution Steps

Apply the distributive property by multiplying each term of x+2 by each term of x+3.

$$\left(x^{2}+3x+2x+6\right)\left(4-x\right)$$

Combine 3x and 2x to get 5x.

$$\left(x^{2}+5x+6\right)\left(4-x\right)$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of 4-x.

$$4x^{2}-x^{3}+20x-5x^{2}+24-6x$$

Combine 4x^{2} and -5x^{2} to get -x^{2}.

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

Combine 20x and -6x to get 14x.

$$-x^{2}-x^{3}+14x+24$$