Day 1 Sample SAT Problem

Yesterday I mentioned how it was important to make sure we are teaching the importance of equivalent expressions and understanding if two expressions are equal to each other. If we have an equation that shows two expressions are equivalent, then we can substitute either side of the equation for the other in any expression.

Here is a sample SAT problem where this concept is critical in solving the problem.

So there is another critical skill that a student must know to be able to solve this problem and that is factoring using Greatest Common Factor. In this problem we can see that the two terms being subtracted share a common factor of xy. Although this problem might seem hard at first by factoring xy from both terms, we can see that the resulting expression contains two expressions that we have an equivalence for. Now we can substitute for both xy and x-y using the two equations that were given to us.

What seems difficult at first sight, might actually be one of the easier problems to solve if we can understand two mathematical skills: Factoring using Greatest Common Factor and Substituting.

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