Question

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

Answer 1

`2axxa^2=2a^3`

Explanation:

`a^m=axxaxxa.....` `m` times.

Hence `2axxa^2`

= `(2xxa)xx(axxa)`

= `2xxaxxaxxa`

= `2a^3`

Answer 2

`2a^3`

Explanation:

`color(blue)("The meaning of "2a)`

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 `2xx "apples"`

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

Then in stead of `2xx"apples"` I would write: `2xxa`

But `2xxa` is the equivalent of saying 2 of apples instead of 2 apples

So instead of writing `2xx a` we write `2a`

So `2a` means the same as `a+a=2xxa`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("The meaning of "a^2)`

Simply put this is the same as `axxa`

In the same way that `a^3` means `axxaxxa`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

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

`2xxa^3->2a^3`