# SAT Math Multiple Choice Question 650: Answer and Explanation

Home > SAT Test > SAT Math Multiple Choice Practice Tests

### Test Information

- Use your browser's back button to return to your test results.
- Do more SAT Math Multiple Choice Practice Tests.

**Question: 650**

**5.** *a*^{4} - 6*a*^{2} + 10

Which of the following is equivalent to the expression shown above?

- A. (
*a*^{2}- 2)(*a*^{2}- 5) - B. (
*a*^{2}- 1)(*a*^{2}- 10) - C. (
*a*^{2}+ 3)^{2}+ 1 - D. (
*a*^{2}- 3)^{2}+ 1

**Correct Answer:** D

**Explanation:**

**D**

**Advanced Mathematics (multiplying polynomials) EASY-MEDIUM**

The simplest way to approach this problem is to "expand" the choices to see which one yields an expression that is equivalent to the original expression. You must remember how to FOIL (Chapter 9, Lesson 4) when multiplying two binomials:

(A) (*a*^{2} - 2)(*a*^{2} - 5) = *a*^{4} - 5*a*^{2} - 2*a*^{2} + 10 = *a*^{4} - 7*a*^{2} + 10

(Close, but no.)

(B) (*a*^{2} - 1)(*a*^{2} - 10) = *a*^{4} - 10*a*^{2} - 1*a*^{2} + 10 = *a*^{4} - 11*a*^{2} + 10

(Close, but no.)

(C) (*a*^{2} + 3)^{2} + 1 = *a*^{4} + 3*a*^{2} + 3*a*^{2} + 9 + 1 = *a*^{4} + 6*a*^{2} + 10

(Close, but no.)

(D) (*a*^{2} - 3)^{2} + 1 = *a*^{4} - 3*a*^{2} - 3*a*^{2} + 9 + 1 = *a*^{4} - 6*a*^{2} + 10

(Yes.)