# How do you simplify (2x + 3y)^3?

May 23, 2018

$\left(2 x + 3 y\right) = \textcolor{b l u e}{8 {x}^{3} + 36 {x}^{2} y + 54 x {y}^{2} + 27 {y}^{3}}$

#### Explanation:

Using Pascal's Triangle to simplify the expansion:
{: (ul("exponent")," | pattern:",,,,,,), (0,,1,,,,,), (1,,1,1,,,,), (2,,1,2,1,,,), (color(lime)3,,color(magenta)1,color(magenta)3,color(magenta)3,color(magenta)1,,), (4,,1,4,6,4,1,), (5,,1,5,10,10,5,1), (...,,...,,,,,) :}

${\left(2 x + 3 y\right)}^{\textcolor{\lim e}{3}}$
$\textcolor{w h i t e}{\text{XXX}} = \textcolor{m a \ge n t a}{1} \cdot {\left(2 x\right)}^{3} \cdot {\left(3 y\right)}^{0} + \textcolor{m a \ge n t a}{3} \cdot {\left(2 x\right)}^{2} \cdot {\left(3 y\right)}^{1} + \textcolor{m a \ge n t a}{3} \cdot {\left(2 x\right)}^{1} \cdot {\left(3 y\right)}^{2} + \textcolor{m a \ge n t a}{1} \cdot {\left(2 x\right)}^{0} \cdot {\left(3 y\right)}^{3}$

$\textcolor{w h i t e}{\text{XXX")=color(white)("XXXXXXX")8x^3 +color(white)("XXXXX")36x^2y +color(white)("XXXXX") 54xy^2+color(white)("XXXXX}} 27 {y}^{3}$