Solve (x+3)(x+8)-(x+1)(x+5)

$$( x + 3 ) ( x + 8 ) - ( x + 1 ) ( x + 5 )$$

Evaluate

$$5x+19$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of x+8.

$$x^{2}+8x+3x+24-\left(x+1\right)\left(x+5\right)$$

Combine 8x and 3x to get 11x.

$$x^{2}+11x+24-\left(x+1\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x+1 by each term of x+5.

$$x^{2}+11x+24-\left(x^{2}+5x+x+5\right)$$

Combine 5x and x to get 6x.

$$x^{2}+11x+24-\left(x^{2}+6x+5\right)$$

To find the opposite of x^{2}+6x+5, find the opposite of each term.

$$x^{2}+11x+24-x^{2}-6x-5$$

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

$$11x+24-6x-5$$

Combine 11x and -6x to get 5x.

$$5x+24-5$$

Subtract 5 from 24 to get 19.

$$5x+19$$

Expand

$$5x+19$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of x+8.

$$x^{2}+8x+3x+24-\left(x+1\right)\left(x+5\right)$$

Combine 8x and 3x to get 11x.

$$x^{2}+11x+24-\left(x+1\right)\left(x+5\right)$$

Apply the distributive property by multiplying each term of x+1 by each term of x+5.

$$x^{2}+11x+24-\left(x^{2}+5x+x+5\right)$$

Combine 5x and x to get 6x.

$$x^{2}+11x+24-\left(x^{2}+6x+5\right)$$

To find the opposite of x^{2}+6x+5, find the opposite of each term.

$$x^{2}+11x+24-x^{2}-6x-5$$

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

$$11x+24-6x-5$$

Combine 11x and -6x to get 5x.

$$5x+24-5$$

Subtract 5 from 24 to get 19.

$$5x+19$$