# What is the standard form of a polynomial 6x(x^2+2x+1)?

Apr 3, 2016

$6 {x}^{3} + 12 {x}^{2} + 6 x$

#### Explanation:

$1$. Use the distributive property, color(red)a(color(blue)b color(violet)(+c))=color(red)acolor(blue)b $\textcolor{red}{+ a} \textcolor{v i o \le t}{c}$, to multiply $6 x$ by each term within the brackets.

color(red)(6x)(color(blue)(x^2) $\textcolor{v i o \le t}{+ 2 x}$ color(darkorange)(+1))

$= \textcolor{red}{6 x} \left(\textcolor{b l u e}{{x}^{2}}\right) \textcolor{red}{+ 6 x} \left(\textcolor{v i o \le t}{2 x}\right) \textcolor{red}{+ 6 x} \left(\textcolor{\mathmr{and} a n \ge}{1}\right)$

$2$. Simplify.

$= \textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} 6 {x}^{3} + 12 {x}^{2} + 6 x \textcolor{w h i t e}{\frac{a}{a}} |}}}$