# SAT Practice Questions: Factoring

The SAT Math exam contains questions where you’ll need to know how to factor down a quadratic equation. The following practice questions ask you to do that, and then to plug in your solution to solve a given expression.

## Practice questions

**What is the value of**

if*a*–*b*= 1/3 and*a*+*b*= 6?**What is the value of***p*^{2}+*q*^{2}if*p*^{2}–*q*^{2}= 7 and*p*^{4}–*q*^{4}= 28?

**A.**2

**B.**3

**C.**4

**D.**5

## Answers and explanations

**The correct answer is 25.**

Remember that*a*^{2 }–*b*^{2}= (*a*+*b*)(*a*–*b*). Plug in the values of*a*+*b*and*a*–*b*to solve for*a*^{2}–*b*^{2}:

Now plug 2 in for*a*^{2}–*b*^{2}:

**The correct answer is Choice (C).**

Start by factoring*p*^{4}–*q*^{4}:

Now plug in the values that the question gives you: