Solve left(-2xright)^2-(-2x+3)(-2x-3)

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

Evaluate

$$9$$

Solution Steps

Expand \left(-2x\right)^{2}.

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

Calculate -2 to the power of 2 and get 4.

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

Consider \left(-2x+3\right)\left(-2x-3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$4x^{2}-\left(\left(-2x\right)^{2}-9\right)$$

Expand \left(-2x\right)^{2}.

$$4x^{2}-\left(\left(-2\right)^{2}x^{2}-9\right)$$

Calculate -2 to the power of 2 and get 4.

$$4x^{2}-\left(4x^{2}-9\right)$$

To find the opposite of 4x^{2}-9, find the opposite of each term.

$$4x^{2}-4x^{2}+9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$9$$

Factor

$$3^{2}$$