# How do you simplify (2ax + 1/2bx)^2 ?

Mar 18, 2018

color(magenta)((x^2(16a^2+8ab+b^2))/4

#### Explanation:

${\left(2 a x + \frac{1}{2} b x\right)}^{2}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$2 a x + \frac{1}{2} b x$
$\textcolor{w h i t e}{a a a a a a a a a a a}$$\times \underline{2 a x + \frac{1}{2} b x}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$4 {a}^{2} {x}^{2} + a b {x}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a a a a}$$a b {x}^{2} + \frac{1}{4} {b}^{2} {x}^{2}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\overline{4 {a}^{2} {x}^{2} + 2 a b {x}^{2} + \frac{1}{4} {b}^{2} {x}^{2}}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = \left(4 {a}^{2} {x}^{2} + 2 a b {x}^{2} + \frac{1}{4} {b}^{2} {x}^{2}\right) \times \frac{4}{4}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$\therefore = \frac{16 {a}^{2} {x}^{2} + 8 a b {x}^{2} + {b}^{2} {x}^{2}}{4}$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$:.color(magenta)(=(x^2(16a^2+8ab+b^2))/4