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

May 28, 2018

$8 {x}^{2} + 9 x$

#### Explanation:

Given -

$\left(6 {x}^{2} + 3 x\right) + \left(2 {x}^{2} + 6 x\right)$
$6 {x}^{2} + 3 x + 2 {x}^{2} + 6 x$
$8 {x}^{2} + 9 x$

May 28, 2018

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

$\left(6 {x}^{2} + 3 x\right) + \left(2 {x}^{2} + 6 x\right) =$
$6 {x}^{2} + 2 {x}^{2} + 3 x + 6 x =$
${x}^{2} \left(6 + 2\right) + x \left(3 + 6\right) =$
8 x^2 + 9x

May 28, 2018

$\left(6 {x}^{2} + 3 x\right) + \left(2 {x}^{2} + 6 x\right) = 8 {x}^{2} + 9 x$

#### Explanation:

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

$a + \left(b + c\right) = \left(a + b\right) + c$

$a + b = b + a$

Multiplication is left and right distributive over addition:

$a \left(b + c\right) = a b + a c$

$\left(a + b\right) c = a c + b c$

Hence we find:

$\left(6 {x}^{2} + 3 x\right) + \left(2 {x}^{2} + 6 x\right)$

$= 6 {x}^{2} + \left(3 x + \left(2 {x}^{2} + 6 x\right)\right) \text{ }$ (by associativity)

$= 6 {x}^{2} + \left(\left(2 {x}^{2} + 6 x\right) + 3 x\right) \text{ }$ (by commutativity)

$= 6 {x}^{2} + \left(2 {x}^{2} + \left(6 x + 3 x\right)\right) \text{ }$ (by associativity)

$= \left(6 {x}^{2} + 2 {x}^{2}\right) + \left(6 x + 3 x\right) \text{ }$ (by associativity)

$= \left(6 + 2\right) {x}^{2} + \left(6 + 3\right) x \text{ }$ (by right distributivity twice)

$= 8 {x}^{2} + 9 x$