Solve (3x+4)(x+1)-(2x+5)(x+4)

$$(3x+4)(x+1)-(2x+5)(x+4)$$

Evaluate

$$\left(x-8\right)\left(x+2\right)$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+4 by each term of x+1.

$$3x^{2}+3x+4x+4-\left(2x+5\right)\left(x+4\right)$$

Combine 3x and 4x to get 7x.

$$3x^{2}+7x+4-\left(2x+5\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x+5 by each term of x+4.

$$3x^{2}+7x+4-\left(2x^{2}+8x+5x+20\right)$$

Combine 8x and 5x to get 13x.

$$3x^{2}+7x+4-\left(2x^{2}+13x+20\right)$$

To find the opposite of 2x^{2}+13x+20, find the opposite of each term.

$$3x^{2}+7x+4-2x^{2}-13x-20$$

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

$$x^{2}+7x+4-13x-20$$

Combine 7x and -13x to get -6x.

$$x^{2}-6x+4-20$$

Subtract 20 from 4 to get -16.

$$x^{2}-6x-16$$

Expand

$$x^{2}-6x-16$$

Solution Steps

Apply the distributive property by multiplying each term of 3x+4 by each term of x+1.

$$3x^{2}+3x+4x+4-\left(2x+5\right)\left(x+4\right)$$

Combine 3x and 4x to get 7x.

$$3x^{2}+7x+4-\left(2x+5\right)\left(x+4\right)$$

Apply the distributive property by multiplying each term of 2x+5 by each term of x+4.

$$3x^{2}+7x+4-\left(2x^{2}+8x+5x+20\right)$$

Combine 8x and 5x to get 13x.

$$3x^{2}+7x+4-\left(2x^{2}+13x+20\right)$$

To find the opposite of 2x^{2}+13x+20, find the opposite of each term.

$$3x^{2}+7x+4-2x^{2}-13x-20$$

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

$$x^{2}+7x+4-13x-20$$

Combine 7x and -13x to get -6x.

$$x^{2}-6x+4-20$$

Subtract 20 from 4 to get -16.

$$x^{2}-6x-16$$