Simplifying Expressions
If a problem contains an expression that can be factored, it is very likely that you will need to factor it to
solve the problem. So, you should always be on the lookout for opportunities to factor. For example, if a
problem contains the expression 2x + 2y, you should see if factoring it to produce the expression 2(x + y)
will help you to solve the problem.
Something to Hide
Because factoring or
expanding is usually the
key to finding the answer
on such problems, learn to
recognize expressions that
could be either factored or
expanded. This will earn
you more points. The test
writers will try to hide the
answer by factoring or
expanding the result.If a problem contains an expression that is already factored, you should consider using the distributive
law to expand it. For example, if a problem contains the expression 2(x + y), you should see if expanding
it to 2x + 2y will help.
Here are five examples that we’ve worked out:
- 4 x + 24 = 4(x) + 4(6) = 4(x + 6)
- = = = 5(x − 6) 5x − 30
3. = = +1
- 2(x + y) + 3(x + y) = (2 + 3)(x + y) = 5(x + y)
- p(r + s) + q(r + s) = (p + q)(r + s)
Here’s how this might be tested on the SAT.
10.Which of the following is equivalent to + f ?A) (f + g)