Question

What is `(6x^2+3x)+(2x^2+6x)`?

Answer 1

`8x^2+9x`

Explanation:

Given -

`(6x^2+3x)+(2x^2+6x)`
`6x^2+3x+2x^2+6x`
`8x^2+9x`

Answer 2

Remove the parentheses and add the x^2 terms together. You get 6x^2 + 2 x^2 = 8 x^2.
Then do the same with the x terms
3x + 6x = 9x

8 x^2 + 9x

In summary

`(6 x^2 + 3x) + (2x^2 + 6x) =`
`6 x^2 + 2x^2 + 3x + 6x =`
`x^2(6+2) + x(3+6) =`
8 x^2 + 9x

Answer 3

`(6x^2+3x)+(2x^2+6x) = 8x^2+9x`

Explanation:

Here is a method of solution demonstrating some fundamental properites of arithmetic:

Addition is associative:

`a+(b+c) = (a+b)+c`

Addition is commutative:

`a+b = b+a`

Multiplication is left and right distributive over addition:

`a(b+c) = ab+ac`

`(a+b)c = ac+bc`

Hence we find:

`(6x^2+3x)+(2x^2+6x)`

`=6x^2+(3x+(2x^2+6x))" "` (by associativity)

`=6x^2+((2x^2+6x)+3x)" "` (by commutativity)

`=6x^2+(2x^2+(6x+3x))" "` (by associativity)

`=(6x^2+2x^2)+(6x+3x)" "` (by associativity)

`=(6+2)x^2+(6+3)x" "` (by right distributivity twice)

`=8x^2+9x`