Solve 4(x+1)(x+2)(x+3)

$$4(x+1)(x+2)(x+3)$$

Expand

$$4x^{3}+24x^{2}+44x+24$$

Solution Steps

Use the distributive property to multiply 4 by x+1.

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

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

$$\left(4x^{2}+8x+4x+8\right)\left(x+3\right)$$

Combine 8x and 4x to get 12x.

$$\left(4x^{2}+12x+8\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of 4x^{2}+12x+8 by each term of x+3.

$$4x^{3}+12x^{2}+12x^{2}+36x+8x+24$$

Combine 12x^{2} and 12x^{2} to get 24x^{2}.

$$4x^{3}+24x^{2}+36x+8x+24$$

Combine 36x and 8x to get 44x.

$$4x^{3}+24x^{2}+44x+24$$

Evaluate

$$4\left(x+1\right)\left(x+2\right)\left(x+3\right)$$

Solution Steps

Use the distributive property to multiply 4 by x+1.

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

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

$$\left(4x^{2}+8x+4x+8\right)\left(x+3\right)$$

Combine 8x and 4x to get 12x.

$$\left(4x^{2}+12x+8\right)\left(x+3\right)$$

Apply the distributive property by multiplying each term of 4x^{2}+12x+8 by each term of x+3.

$$4x^{3}+12x^{2}+12x^{2}+36x+8x+24$$

Combine 12x^{2} and 12x^{2} to get 24x^{2}.

$$4x^{3}+24x^{2}+36x+8x+24$$

Combine 36x and 8x to get 44x.

$$4x^{3}+24x^{2}+44x+24$$