Solve left(-2xright)^2-(2x+5)(2x-5)

$${ \left(-2x \right) }^{ 2 } -(2x+5)(2x-5)$$

Evaluate

$$25$$

Solution Steps

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

$$\left(-2\right)^{2}x^{2}-\left(2x+5\right)\left(2x-5\right)$$

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

$$4x^{2}-\left(2x+5\right)\left(2x-5\right)$$

Consider \left(2x+5\right)\left(2x-5\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 5.

$$4x^{2}-\left(\left(2x\right)^{2}-25\right)$$

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

$$4x^{2}-\left(2^{2}x^{2}-25\right)$$

Calculate 2 to the power of 2 and get 4.

$$4x^{2}-\left(4x^{2}-25\right)$$

To find the opposite of 4x^{2}-25, find the opposite of each term.

$$4x^{2}-4x^{2}+25$$

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

$$25$$

Factor

$$5^{2}$$