Solve (x+3)(x-7)-x(x-1)

$$( x + 3 ) ( x - 7 ) - x ( x - 1 )$$

Evaluate

$$-3x-21$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of x-7.

$$x^{2}-7x+3x-21-x\left(x-1\right)$$

Combine -7x and 3x to get -4x.

$$x^{2}-4x-21-x\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$x^{2}-4x-21-\left(x^{2}-x\right)$$

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

$$x^{2}-4x-21-x^{2}-\left(-x\right)$$

The opposite of -x is x.

$$x^{2}-4x-21-x^{2}+x$$

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

$$-4x-21+x$$

Combine -4x and x to get -3x.

$$-3x-21$$

Expand

$$-3x-21$$

Solution Steps

Apply the distributive property by multiplying each term of x+3 by each term of x-7.

$$x^{2}-7x+3x-21-x\left(x-1\right)$$

Combine -7x and 3x to get -4x.

$$x^{2}-4x-21-x\left(x-1\right)$$

Use the distributive property to multiply x by x-1.

$$x^{2}-4x-21-\left(x^{2}-x\right)$$

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

$$x^{2}-4x-21-x^{2}-\left(-x\right)$$

The opposite of -x is x.

$$x^{2}-4x-21-x^{2}+x$$

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

$$-4x-21+x$$

Combine -4x and x to get -3x.

$$-3x-21$$