How do you simplify $2 a \times a^{2}$ $2a times a^2$ ?

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Answer 1 · 2016-06-24T05:26:01

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

$a^m=axxaxxa.....$ $m$ times.

Hence $2axxa^2$

= $(2xxa)xx(axxa)$

= $2xxaxxaxxa$

= $2a^3$

Answer 2 · 2016-06-25T17:02:28

$2a^3$

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

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 $axxaxxa$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$color(blue)("Putting it all together")$

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

$2xxa^3->2a^3$

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