Solve (n-2sqrt{x})(n+2sqrt{x})

$$( n - 2 \sqrt { x } ) ( n + 2 \sqrt { x } )$$

Evaluate

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

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}.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

Differentiate w.r.t. x

$$-4$$