Solve frac{sqrt{2}(4-x)}{2}*x/sqrt{2}

$$\frac { \sqrt { 2 } ( 4 - x ) } { 2 } \times \frac { x } { \sqrt { 2 } }$$

Evaluate

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

Solution Steps

Use the distributive property to multiply \sqrt{2} by 4-x.

$$\frac{4\sqrt{2}-\sqrt{2}x}{2}\times \frac{x}{\sqrt{2}}$$

Rationalize the denominator of \frac{x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

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

The square of \sqrt{2} is 2.

$$\frac{4\sqrt{2}-\sqrt{2}x}{2}\times \frac{x\sqrt{2}}{2}$$

Multiply \frac{4\sqrt{2}-\sqrt{2}x}{2} times \frac{x\sqrt{2}}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(4\sqrt{2}-\sqrt{2}x\right)x\sqrt{2}}{2\times 2}$$

Multiply 2 and 2 to get 4.

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

Use the distributive property to multiply 4\sqrt{2}-\sqrt{2}x by x.

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

Use the distributive property to multiply 4\sqrt{2}x-\sqrt{2}x^{2} by \sqrt{2}.

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

The square of \sqrt{2} is 2.

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

Multiply 4 and 2 to get 8.

$$\frac{8x-x^{2}\left(\sqrt{2}\right)^{2}}{4}$$

The square of \sqrt{2} is 2.

$$\frac{8x-x^{2}\times 2}{4}$$

Multiply -1 and 2 to get -2.

$$\frac{8x-2x^{2}}{4}$$

Differentiate w.r.t. x

$$2-x$$