Solve (x+8)(2x+5)-(x+8)(x+2)

$$( x + 8 ) ( 2 x + 5 ) - ( x + 8 ) ( x + 2 )$$

Evaluate

$$\left(x+3\right)\left(x+8\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+8 by each term of 2x+5.

$$2x^{2}+5x+16x+40-\left(x+8\right)\left(x+2\right)$$

Combine 5x and 16x to get 21x.

$$2x^{2}+21x+40-\left(x+8\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x+8 by each term of x+2.

$$2x^{2}+21x+40-\left(x^{2}+2x+8x+16\right)$$

Combine 2x and 8x to get 10x.

$$2x^{2}+21x+40-\left(x^{2}+10x+16\right)$$

To find the opposite of x^{2}+10x+16, find the opposite of each term.

$$2x^{2}+21x+40-x^{2}-10x-16$$

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

$$x^{2}+21x+40-10x-16$$

Combine 21x and -10x to get 11x.

$$x^{2}+11x+40-16$$

Subtract 16 from 40 to get 24.

$$x^{2}+11x+24$$

Expand

$$x^{2}+11x+24$$

Solution Steps

Apply the distributive property by multiplying each term of x+8 by each term of 2x+5.

$$2x^{2}+5x+16x+40-\left(x+8\right)\left(x+2\right)$$

Combine 5x and 16x to get 21x.

$$2x^{2}+21x+40-\left(x+8\right)\left(x+2\right)$$

Apply the distributive property by multiplying each term of x+8 by each term of x+2.

$$2x^{2}+21x+40-\left(x^{2}+2x+8x+16\right)$$

Combine 2x and 8x to get 10x.

$$2x^{2}+21x+40-\left(x^{2}+10x+16\right)$$

To find the opposite of x^{2}+10x+16, find the opposite of each term.

$$2x^{2}+21x+40-x^{2}-10x-16$$

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

$$x^{2}+21x+40-10x-16$$

Combine 21x and -10x to get 11x.

$$x^{2}+11x+40-16$$

Subtract 16 from 40 to get 24.

$$x^{2}+11x+24$$