Solve 1x^2+4x/sqrt{2}

$$\frac { 1 x ^ { 2 } + 4 x } { \sqrt { 2 } }$$

Factor

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

Solution Steps

Rationalize the denominator of \frac{1x^{2}+4x}{\sqrt{2}} by multiplying numerator and denominator by \sqrt{2}.

$$factor(\frac{\left(1x^{2}+4x\right)\sqrt{2}}{\left(\sqrt{2}\right)^{2}})$$

The square of \sqrt{2} is 2.

$$factor(\frac{\left(1x^{2}+4x\right)\sqrt{2}}{2})$$

Use the distributive property to multiply 1x^{2}+4x by \sqrt{2}.

$$factor(\frac{1x^{2}\sqrt{2}+4x\sqrt{2}}{2})$$

Consider x^{2}\sqrt{2}+4x\sqrt{2}. Factor out x\sqrt{2}.

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

Rewrite the complete factored expression.

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

Evaluate

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