Question

How do you simplify `4a+5a^2+2a^2+a^2`?

Answer 1

`4a+8a^2`

Explanation:

Terms which are raised to the same power of the unknown can be added together. In this case, we have 3 terms to the power of "2" and one term to the power of "1".

Hence we can add the common terms: `5a^2 + 2a^2 + a^2=8a^2` Then we simply add the remained which we can not add. Hence:

`4a+8a^2`

Answer 2

That can be simplified into `a(8a+4)` or `8a^2+4a`

Explanation:

Start by adding the like terms together, that is (terms of `a^2`)
`5a^2+2a^2+a^2 = 8a^2`

Now you can rewrite it as `4a + 8a^2`

The key here is that you can always add the like terms..
For example,

`6x^2 + 3x + 4x^2 + 2x + 3y + 3y^2`
Here all the `x^2` terms can be added together, all the `x` terms can be added together, all the `y` terms can be added together and all the `y^2` terms can be added together..

So we get
`10x^2 + 5x + 3y^2 + 3y`

Can be simplified even further by factoring out the `5x` from first 2 terms and `3y` from the next two terms,
`5x(2x+1) + 3y(y+1)`