Solve (5sqrt{x}+2y)(5sqrt{x}-2y)

$$( 5 \sqrt { x } + 2 y ) ( 5 \sqrt { x } - 2 y )$$

Evaluate

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

Solution Steps

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

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

Expand \left(5\sqrt{x}\right)^{2}.

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

Calculate 5 to the power of 2 and get 25.

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

Calculate \sqrt{x} to the power of 2 and get x.

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

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

$$25x-2^{2}y^{2}$$

Calculate 2 to the power of 2 and get 4.

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

Differentiate w.r.t. x

$$25$$