# How do you write 6x^2 + 4x  in factored form?

Mar 21, 2018

color(green)(=> (sqrt6 x + 2 / sqrt6)^2 - 2/3

=> color(red)((sqrt6 x + 2/sqrt6 + sqrt(2/3)) * (sqrt6 x + 2/sqrt6 - sqrt(2/3))

#### Explanation:

$6 {x}^{2} + 4 x = 6 x \cdot 2 + 4 x + \frac{4}{6} - \frac{4}{6} , \text{ Add & Subtract 4/6}$

$\implies {\left(\sqrt{6} x\right)}^{2} + 2 \cdot \left(\frac{1}{\sqrt{6}}\right) \cdot 2 \cdot x + {\left(\frac{2}{\sqrt{6}}\right)}^{2} - \frac{2}{3}$

It is in the form$\left(a 2 + 2 a b + {b}^{2}\right) \text{ where } a = \sqrt{6.} b = \frac{2}{\sqrt{6}}$

Hence $\implies {\left(\sqrt{6} x + \frac{2}{\sqrt{6}}\right)}^{2} - {\left(\sqrt{\frac{2}{3}}\right)}^{2}$

It is again in the for ${a}^{2} - {b}^{2}$

$\implies \left(\sqrt{6} x + \frac{2}{\sqrt{6}} + \sqrt{\frac{2}{3}}\right) \cdot \left(\sqrt{6} x + \frac{2}{\sqrt{6}} - \sqrt{\frac{2}{3}}\right)$

Mar 21, 2018

$2 x \left(3 x + 2\right)$

#### Explanation:

$\text{take out a "color(blue)"common factor } 2 x$

$\Rightarrow 6 {x}^{2} + 4 x = 2 x \left(3 x + 2\right)$