# How do you simplify 2a times a^2?

Jun 24, 2016

$2 a \times {a}^{2} = 2 {a}^{3}$

#### Explanation:

${a}^{m} = a \times a \times a \ldots . .$ $m$ times.

Hence $2 a \times {a}^{2}$

= $\left(2 \times a\right) \times \left(a \times a\right)$

= $2 \times a \times a \times a$

= $2 {a}^{3}$

Jun 25, 2016

$2 {a}^{3}$

#### Explanation:

$\textcolor{b l u e}{\text{The meaning of } 2 a}$

Consider the use of language that states: "I have got 2 apples".

We do not say 2 of apples or any other variant other than 2 apples.

Mathematically this is the equivalent of $2 \times \text{apples}$

Suppose I declare: Let the object "apples" be represented by $a$

Then in stead of $2 \times \text{apples}$ I would write: $2 \times a$

But $2 \times a$ is the equivalent of saying 2 of apples instead of 2 apples

So instead of writing $2 \times a$ we write $2 a$

So $2 a$ means the same as $a + a = 2 \times a$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{The meaning of } {a}^{2}}$

Simply put this is the same as $a \times a$

In the same way that ${a}^{3}$ means $a \times a \times a$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

color(brown)(2a)color(green)(xxa^2)color(brown)(->2xxacolor(green)(xxaxxa)

$2 \times {a}^{3} \to 2 {a}^{3}$