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

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

Evaluate

$$-5x^{2}-14x-5$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of 2x+4 by each term of x+3.

$$2x^{2}+6x+4x+12-3\left(x+1\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

Combine 6x and 4x to get 10x.

$$2x^{2}+10x+12-3\left(x+1\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

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

$$2x^{2}+10x+12+\left(-3x-3\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

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

$$2x^{2}+10x+12-3x^{2}-9x-3x-9-4\left(x+1\right)\left(x+2\right)$$

Combine -9x and -3x to get -12x.

$$2x^{2}+10x+12-3x^{2}-12x-9-4\left(x+1\right)\left(x+2\right)$$

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

$$-x^{2}+10x+12-12x-9-4\left(x+1\right)\left(x+2\right)$$

Combine 10x and -12x to get -2x.

$$-x^{2}-2x+12-9-4\left(x+1\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$-x^{2}-2x+3-4\left(x+1\right)\left(x+2\right)$$

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

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

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

$$-x^{2}-2x+3-4x^{2}-8x-4x-8$$

Combine -8x and -4x to get -12x.

$$-x^{2}-2x+3-4x^{2}-12x-8$$

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

$$-5x^{2}-2x+3-12x-8$$

Combine -2x and -12x to get -14x.

$$-5x^{2}-14x+3-8$$

Subtract 8 from 3 to get -5.

$$-5x^{2}-14x-5$$

Expand

$$-5x^{2}-14x-5$$

Solution Steps

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

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

Apply the distributive property by multiplying each term of 2x+4 by each term of x+3.

$$2x^{2}+6x+4x+12-3\left(x+1\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

Combine 6x and 4x to get 10x.

$$2x^{2}+10x+12-3\left(x+1\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

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

$$2x^{2}+10x+12+\left(-3x-3\right)\left(x+3\right)-4\left(x+1\right)\left(x+2\right)$$

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

$$2x^{2}+10x+12-3x^{2}-9x-3x-9-4\left(x+1\right)\left(x+2\right)$$

Combine -9x and -3x to get -12x.

$$2x^{2}+10x+12-3x^{2}-12x-9-4\left(x+1\right)\left(x+2\right)$$

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

$$-x^{2}+10x+12-12x-9-4\left(x+1\right)\left(x+2\right)$$

Combine 10x and -12x to get -2x.

$$-x^{2}-2x+12-9-4\left(x+1\right)\left(x+2\right)$$

Subtract 9 from 12 to get 3.

$$-x^{2}-2x+3-4\left(x+1\right)\left(x+2\right)$$

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

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

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

$$-x^{2}-2x+3-4x^{2}-8x-4x-8$$

Combine -8x and -4x to get -12x.

$$-x^{2}-2x+3-4x^{2}-12x-8$$

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

$$-5x^{2}-2x+3-12x-8$$

Combine -2x and -12x to get -14x.

$$-5x^{2}-14x+3-8$$

Subtract 8 from 3 to get -5.

$$-5x^{2}-14x-5$$