Solve {l}{(4+x)(x-4)}{-(x-3)(x-5)}

$$\left. \begin{array} { l } { ( 4 + x ) ( x - 4 ) } \\ { - ( x - 3 ) ( x - 5 ) } \end{array} \right.$$

Evaluate

$$8x-31$$

Solution Steps

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

$$4x-16+x^{2}-4x-\left(x-3\right)\left(x-5\right)$$

Combine 4x and -4x to get 0.

$$-16+x^{2}-\left(x-3\right)\left(x-5\right)$$

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

$$-16+x^{2}-\left(x^{2}-5x-3x+15\right)$$

Combine -5x and -3x to get -8x.

$$-16+x^{2}-\left(x^{2}-8x+15\right)$$

To find the opposite of x^{2}-8x+15, find the opposite of each term.

$$-16+x^{2}-x^{2}-\left(-8x\right)-15$$

The opposite of -8x is 8x.

$$-16+x^{2}-x^{2}+8x-15$$

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

$$-16+8x-15$$

Subtract 15 from -16 to get -31.

$$-31+8x$$

Expand

$$8x-31$$

Solution Steps

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

$$4x-16+x^{2}-4x-\left(x-3\right)\left(x-5\right)$$

Combine 4x and -4x to get 0.

$$-16+x^{2}-\left(x-3\right)\left(x-5\right)$$

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

$$-16+x^{2}-\left(x^{2}-5x-3x+15\right)$$

Combine -5x and -3x to get -8x.

$$-16+x^{2}-\left(x^{2}-8x+15\right)$$

To find the opposite of x^{2}-8x+15, find the opposite of each term.

$$-16+x^{2}-x^{2}-\left(-8x\right)-15$$

The opposite of -8x is 8x.

$$-16+x^{2}-x^{2}+8x-15$$

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

$$-16+8x-15$$

Subtract 15 from -16 to get -31.

$$-31+8x$$