I’ve said it before and I’ll say it again: the writers of standardized tests assess the same concepts, over and over and over again.  Test experts are able to become test experts for that very reason—there is a finite amount of material one needs to learn in order to master the ACT and the SAT. If you study a few dozen tests and find these predictable patterns, you could be an expert, too.

Luckily, I’m here to save you from that mind-numbing task. And trust me—it’s mind-numbing, especially when we get into some of the concepts from Algebra II, such as classic quadratic forms.This week’s tip comes from the Math section and looks at three common quadratic forms on the ACT and SAT:

         1.            (x + y)(x – y)  =  x² – y²

                         Examples:

                        (t + 5)(t – 5)   =  t² – 5²   =   t² – 25

                        (3a + b)(3a – b)  =  (3a)² – b²  =  9a² – b²

                        y² – 64  =  (y + 8)(y – 8)

                        36 – n²  =  (6 + n)(6 – n)

        2.            (x + y)²  =  x² + 2xy + y²

                        Examples:

                        (t + 5)²  =  t² + 2(t)(5) + 5²  =  t² + 10t + 25

                        (3a + b)²  =  (3a)² + 2(3a)(b) + b²  =  9a² + 6ab + b²

                        (6 + n)²  = 6² + 2(6)(n) + n²  = 36 + 12n + n²

        3.            (x – y)²  =  x² – 2xy + y²

                        Examples:

                        (t – 5)²  =  t² – 2(t)(5) + 5²  =  t² – 10t + 25

                        (3a – b)²  =  (3a)² – 2(3a)(b) + b²  =  9a² – 6ab + b²

                        (6 – n)²   = 6² – 2(6)(n) + n²  = 36 – 12n + n²