Distributing eliminates parentheses, and factoring creates them. It’s your job as a Math IC mathematician to decide which technique will best help you solve a problem.
Let’s see a few examples:
Combining Like Terms
After factoring and distributing, there are additional steps you can take to simplify expressions or equations. Combining like terms is one of the simpler techniques you can use, and involves adding or subtracting the coefficients of variables that are raised to the same power. For example, by combining like terms, the expression:
can be simplified to:
by adding the coefficients of the variable x3 together and the coefficients of x2 together.
Generally speaking, when you have an expression in which one variable is raised to the same power in different terms, you can factor out the variable and add or subtract the coefficients, combining them into one coefficient and therefore combining the “like” terms into one term. A general formula for combining like pairs looks something like this:
