Solve (x+10)(x+8)-(x+3)(x+1)

$$(x+10)(x+8)-(x+3)(x+1)$$

Evaluate

$$14x+77$$

Solution Steps

Apply the distributive property by multiplying each term of x+10 by each term of x+8.

$$x^{2}+8x+10x+80-\left(x+3\right)\left(x+1\right)$$

Combine 8x and 10x to get 18x.

$$x^{2}+18x+80-\left(x+3\right)\left(x+1\right)$$

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

$$x^{2}+18x+80-\left(x^{2}+x+3x+3\right)$$

Combine x and 3x to get 4x.

$$x^{2}+18x+80-\left(x^{2}+4x+3\right)$$

To find the opposite of x^{2}+4x+3, find the opposite of each term.

$$x^{2}+18x+80-x^{2}-4x-3$$

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

$$18x+80-4x-3$$

Combine 18x and -4x to get 14x.

$$14x+80-3$$

Subtract 3 from 80 to get 77.

$$14x+77$$

Expand

$$14x+77$$

Solution Steps

Apply the distributive property by multiplying each term of x+10 by each term of x+8.

$$x^{2}+8x+10x+80-\left(x+3\right)\left(x+1\right)$$

Combine 8x and 10x to get 18x.

$$x^{2}+18x+80-\left(x+3\right)\left(x+1\right)$$

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

$$x^{2}+18x+80-\left(x^{2}+x+3x+3\right)$$

Combine x and 3x to get 4x.

$$x^{2}+18x+80-\left(x^{2}+4x+3\right)$$

To find the opposite of x^{2}+4x+3, find the opposite of each term.

$$x^{2}+18x+80-x^{2}-4x-3$$

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

$$18x+80-4x-3$$

Combine 18x and -4x to get 14x.

$$14x+80-3$$

Subtract 3 from 80 to get 77.

$$14x+77$$