GRE Algebra - Adding and Subtracting equations
In the course of solving some of the harder GRE algebra questions, you'll be asked to add or subtract equations so that you can combine terms. For example:
What is the sum of 3x2-2y and 3y2-2z-2x2?
Seems a little tricky? Not at all. What you must remember when adding or subtracting equations is that you can only add or subtract like terms. What exactly does that mean, and how can you ADD x's and y's? It simply means
that you can't add x's to y's, z's to x's, z's to y's, etc. Also, it means that you can only add the same variables of the same power. For example, you can add 3x and 2x, which equals 5x, but you can't add 3x and 2x2 because the xs are
not of the same power.
If ever you need to add, subtract, multiply or divide polynomials, remember that you can only combine LIKE terms.
To solve the above equation (or polynomial addition problem):
||What is the sum of 3x2-2y and
||Rearrange the summation problem and place like terms next to each other so that you know what to add or subtract. Notice that -2y and 3y2 are not like terms, so we cannot combine them.
||(3x2 +(-2x2)) + (-2y) + (-2z) + (3y2)
||Perform the addition or subtraction of like terms.
||(x2 ) + (-2y) + (-2z) + (3y2)
||To simplify, you may need to get rid of the parentheses, keeping in mind that +(-2y), for example, is the same as -2y.
||x2 -2y -2z + 3y2