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

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

Evaluate

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

Solution Steps

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}.

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply x by 4-x.

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

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

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

The opposite of -x^{2} is x^{2}.

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

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

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

Expand

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

Solution Steps

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}.

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

Calculate 2 to the power of 2 and get 4.

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

Use the distributive property to multiply x by 4-x.

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

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

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

The opposite of -x^{2} is x^{2}.

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

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

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