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

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

Evaluate

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

Solution Steps

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

$$\left(x^{2}+2x+3x+6\right)\left(x+1\right)+\left(x+2\right)\left(x+1\right)+x+1$$

Combine 2x and 3x to get 5x.

$$\left(x^{2}+5x+6\right)\left(x+1\right)+\left(x+2\right)\left(x+1\right)+x+1$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of x+1.

$$x^{3}+x^{2}+5x^{2}+5x+6x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Combine x^{2} and 5x^{2} to get 6x^{2}.

$$x^{3}+6x^{2}+5x+6x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Combine 5x and 6x to get 11x.

$$x^{3}+6x^{2}+11x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Apply the distributive property by multiplying each term of x+2 by each term of x+1.

$$x^{3}+6x^{2}+11x+6+x^{2}+x+2x+2+x+1$$

Combine x and 2x to get 3x.

$$x^{3}+6x^{2}+11x+6+x^{2}+3x+2+x+1$$

Combine 6x^{2} and x^{2} to get 7x^{2}.

$$x^{3}+7x^{2}+11x+6+3x+2+x+1$$

Combine 11x and 3x to get 14x.

$$x^{3}+7x^{2}+14x+6+2+x+1$$

Add 6 and 2 to get 8.

$$x^{3}+7x^{2}+14x+8+x+1$$

Combine 14x and x to get 15x.

$$x^{3}+7x^{2}+15x+8+1$$

Add 8 and 1 to get 9.

$$x^{3}+7x^{2}+15x+9$$

Expand

$$x^{3}+7x^{2}+15x+9$$

Solution Steps

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

$$\left(x^{2}+2x+3x+6\right)\left(x+1\right)+\left(x+2\right)\left(x+1\right)+x+1$$

Combine 2x and 3x to get 5x.

$$\left(x^{2}+5x+6\right)\left(x+1\right)+\left(x+2\right)\left(x+1\right)+x+1$$

Apply the distributive property by multiplying each term of x^{2}+5x+6 by each term of x+1.

$$x^{3}+x^{2}+5x^{2}+5x+6x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Combine x^{2} and 5x^{2} to get 6x^{2}.

$$x^{3}+6x^{2}+5x+6x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Combine 5x and 6x to get 11x.

$$x^{3}+6x^{2}+11x+6+\left(x+2\right)\left(x+1\right)+x+1$$

Apply the distributive property by multiplying each term of x+2 by each term of x+1.

$$x^{3}+6x^{2}+11x+6+x^{2}+x+2x+2+x+1$$

Combine x and 2x to get 3x.

$$x^{3}+6x^{2}+11x+6+x^{2}+3x+2+x+1$$

Combine 6x^{2} and x^{2} to get 7x^{2}.

$$x^{3}+7x^{2}+11x+6+3x+2+x+1$$

Combine 11x and 3x to get 14x.

$$x^{3}+7x^{2}+14x+6+2+x+1$$

Add 6 and 2 to get 8.

$$x^{3}+7x^{2}+14x+8+x+1$$

Combine 14x and x to get 15x.

$$x^{3}+7x^{2}+15x+8+1$$

Add 8 and 1 to get 9.

$$x^{3}+7x^{2}+15x+9$$