# How do you add (7x ^ { 3} - 5x ^ { 2} + 9x + 3) + ( 5x ^ { 3} - 7x ^ { 2} - x + 3)?

Dec 18, 2017

$12 {x}^{3} - 12 {x}^{2} + 8 + 6$

#### Explanation:

$\left(7 {x}^{3} - 5 {x}^{2} + 9 x + 3\right) + \left(5 {x}^{3} - 7 {x}^{2} - x + 3\right)$

This is the same as $7 {x}^{3} - 5 {x}^{2} + 9 x + 3 + 5 {x}^{3} - 7 {x}^{2} - x + 3$.

The first thing we do is look for "like terms" and variables with the same degree. Our only variable here is $x$. We have ${x}^{3}$, ${x}^{2}$, $x$, and numbers.

Let's first combine the ${x}^{3}$ values. We have $7 {x}^{3}$ and $5 {x}^{3}$.
$7 {x}^{3} + 5 {x}^{3} = 12 {x}^{3}$

Now ${x}^{2}$:
$- 5 {x}^{2} - 7 {x}^{2} = - 12 {x}^{2}$

$x$:
$9 x - x = 8 x$

Numbers:
$3 + 3 = 6$

Now that we have simplified/combined each of the terms, let's put them together:
$12 {x}^{3} - 12 {x}^{2} + 8 x + 6$