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

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

Evaluate

$$6\left(x+2\right)$$

Solution Steps

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x+3\right)-3\left(x+1\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of 3x+6 by each term of x+3.

$$3x^{2}+9x+6x+18-3\left(x+1\right)\left(x+2\right)$$

Combine 9x and 6x to get 15x.

$$3x^{2}+15x+18-3\left(x+1\right)\left(x+2\right)$$

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

$$3x^{2}+15x+18+\left(-3x-3\right)\left(x+2\right)$$

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

$$3x^{2}+15x+18-3x^{2}-6x-3x-6$$

Combine -6x and -3x to get -9x.

$$3x^{2}+15x+18-3x^{2}-9x-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$15x+18-9x-6$$

Combine 15x and -9x to get 6x.

$$6x+18-6$$

Subtract 6 from 18 to get 12.

$$6x+12$$

Expand

$$6x+12$$

Solution Steps

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x+3\right)-3\left(x+1\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of 3x+6 by each term of x+3.

$$3x^{2}+9x+6x+18-3\left(x+1\right)\left(x+2\right)$$

Combine 9x and 6x to get 15x.

$$3x^{2}+15x+18-3\left(x+1\right)\left(x+2\right)$$

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

$$3x^{2}+15x+18+\left(-3x-3\right)\left(x+2\right)$$

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

$$3x^{2}+15x+18-3x^{2}-6x-3x-6$$

Combine -6x and -3x to get -9x.

$$3x^{2}+15x+18-3x^{2}-9x-6$$

Combine 3x^{2} and -3x^{2} to get 0.

$$15x+18-9x-6$$

Combine 15x and -9x to get 6x.

$$6x+18-6$$

Subtract 6 from 18 to get 12.

$$6x+12$$