PSAT/NMSQT Prep 2022 - Eggert M.D., Strelka A. 2022

Classic quadratics
Quadratics
Passport to advanced math

LEARNING OBJECTIVE

After this lesson, you will be able to:

· Recognize the classic quadratics

To answer a question like this:

Which of the following expressions is equivalent to 36x⁴y⁶ − 4?

A. 6(x⁴y⁶ − 2)

B. −6(x²y³ + 2)

C. (6x²y² − 2)(6x²y² + 2)

D. (6x²y³ − 2)(6x²y³ + 2)

You need to know this:

Memorizing the following classic quadratics will save you time on test day:

o This is known as a “difference of squares” because it takes the form of one perfect square minus another perfect square.

You need to do this:

When you see a pattern that matches either the left or the right side of one of the above equations, simplify by substituting its equivalent form. For example, say you need to simplify the following:

You would substitute (a − b)(a − b) for the numerator and cancel to find that the expression simplifies to a − b:

Explanation:

The expression 36x⁴ y⁶ − 4 is a difference of perfect squares. The square root of 36x⁴ y⁶ is 6x²y³ and the square root of 4 is 2, so the correct factors are . Hence, (D) is correct.

Try on Your Own

Directions: Take as much time as you need on these questions. Work carefully and methodically. There will be an opportunity for timed practice at the end of the chapter.

HINT: What can you do to make (a − b)² in Q6 easier to work with?

6. For all a and b, what is the product of (a − b)² and (a + b)?

A. a² − b²

B.a³ − b³

C.a³ − ab² + a²b − b³

D. a³ − ab² − a²b + b³

7. Which equation does NOT have a solution at x = −4?