# How do you combine (2x - 3 +7x^2) - (3 - 9x^2 - 2x)?

May 9, 2015

Step 1.
Open the parenthesis.
If in front of parenthesis there is a sign plus ($+$) or no sign at all you can open parenthesis as is, retaining all signs of each member inside.
If there is a sign minus ($-$) in front of parenthesis, all signs inside the parenthesis should be changed to opposite and then drop the parenthesis.
As a result, our expression will look like
$2 x - 3 + 7 {x}^{2} - 3 + 9 {x}^{2} + 2 x$

Step 2.
Using commutative law ($a + b = b + a$) of addition and subtraction, regroup the members so that members with $x$ in the same power are next to each other and so are free members (constants):
$7 {x}^{2} + 9 {x}^{2} + 2 x + 2 x - 3 - 3$

Step 3.
Using distributive law ($a \cdot c + b \cdot c = \left(a + b\right) \cdot c$) consolidate members with $x$ in the same power:
$\left(7 + 9\right) {x}^{2} + \left(2 + 2\right) x - 6$

Step 4.
Final simplification:
$16 {x}^{2} + 4 x - 6$