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

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

Evaluate

$$7x+19$$

Solution Steps

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

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

Combine x and 4x to get 5x.

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

Apply the distributive property by multiplying each term of x+3 by each term of x-5.

$$5x+x^{2}+4-\left(x^{2}-5x+3x-15\right)$$

Combine -5x and 3x to get -2x.

$$5x+x^{2}+4-\left(x^{2}-2x-15\right)$$

To find the opposite of x^{2}-2x-15, find the opposite of each term.

$$5x+x^{2}+4-x^{2}-\left(-2x\right)-\left(-15\right)$$

The opposite of -2x is 2x.

$$5x+x^{2}+4-x^{2}+2x-\left(-15\right)$$

The opposite of -15 is 15.

$$5x+x^{2}+4-x^{2}+2x+15$$

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

$$5x+4+2x+15$$

Combine 5x and 2x to get 7x.

$$7x+4+15$$

Add 4 and 15 to get 19.

$$7x+19$$

Expand

$$7x+19$$

Solution Steps

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

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

Combine x and 4x to get 5x.

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

Apply the distributive property by multiplying each term of x+3 by each term of x-5.

$$5x+x^{2}+4-\left(x^{2}-5x+3x-15\right)$$

Combine -5x and 3x to get -2x.

$$5x+x^{2}+4-\left(x^{2}-2x-15\right)$$

To find the opposite of x^{2}-2x-15, find the opposite of each term.

$$5x+x^{2}+4-x^{2}-\left(-2x\right)-\left(-15\right)$$

The opposite of -2x is 2x.

$$5x+x^{2}+4-x^{2}+2x-\left(-15\right)$$

The opposite of -15 is 15.

$$5x+x^{2}+4-x^{2}+2x+15$$

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

$$5x+4+2x+15$$

Combine 5x and 2x to get 7x.

$$7x+4+15$$

Add 4 and 15 to get 19.

$$7x+19$$