Solve (x-3)(x-4)-(x+2)(x-2)

$$( x - 3 ) ( x - 4 ) - ( x + 2 ) ( x - 2 )$$

Evaluate

$$16-7x$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x-4.

$$x^{2}-4x-3x+12-\left(x+2\right)\left(x-2\right)$$

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

$$x^{2}-7x+12-\left(x+2\right)\left(x-2\right)$$

Consider \left(x+2\right)\left(x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-7x+12-\left(x^{2}-2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-7x+12-\left(x^{2}-4\right)$$

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

$$x^{2}-7x+12-x^{2}-\left(-4\right)$$

The opposite of -4 is 4.

$$x^{2}-7x+12-x^{2}+4$$

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

$$-7x+12+4$$

Add 12 and 4 to get 16.

$$-7x+16$$

Expand

$$16-7x$$

Solution Steps

Apply the distributive property by multiplying each term of x-3 by each term of x-4.

$$x^{2}-4x-3x+12-\left(x+2\right)\left(x-2\right)$$

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

$$x^{2}-7x+12-\left(x+2\right)\left(x-2\right)$$

Consider \left(x+2\right)\left(x-2\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}.

$$x^{2}-7x+12-\left(x^{2}-2^{2}\right)$$

Calculate 2 to the power of 2 and get 4.

$$x^{2}-7x+12-\left(x^{2}-4\right)$$

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

$$x^{2}-7x+12-x^{2}-\left(-4\right)$$

The opposite of -4 is 4.

$$x^{2}-7x+12-x^{2}+4$$

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

$$-7x+12+4$$

Add 12 and 4 to get 16.

$$-7x+16$$