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

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

Evaluate

$$2x\left(x-7\right)$$

Solution Steps

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

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

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

$$x^{2}-4x-21+\left(x-7\right)\left(x-3\right)$$

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

$$x^{2}-4x-21+x^{2}-3x-7x+21$$

Combine -3x and -7x to get -10x.

$$x^{2}-4x-21+x^{2}-10x+21$$

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

$$2x^{2}-4x-21-10x+21$$

Combine -4x and -10x to get -14x.

$$2x^{2}-14x-21+21$$

Add -21 and 21 to get 0.

$$2x^{2}-14x$$

Expand

$$2x^{2}-14x$$

Solution Steps

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

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

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

$$x^{2}-4x-21+\left(x-7\right)\left(x-3\right)$$

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

$$x^{2}-4x-21+x^{2}-3x-7x+21$$

Combine -3x and -7x to get -10x.

$$x^{2}-4x-21+x^{2}-10x+21$$

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

$$2x^{2}-4x-21-10x+21$$

Combine -4x and -10x to get -14x.

$$2x^{2}-14x-21+21$$

Add -21 and 21 to get 0.

$$2x^{2}-14x$$