The math tutor recommends a little light factoring on this beautiful Sunday morning….

Last post I discussed common factor, which we will be using in concert with difference of squares. Difference of squares factors x² – 36 into (x + 6)(x – 6). By the foil method you can confirm:

F: x*x=x²

O: x*-6=-6x

I: 6*x=6x

L: 6*-6=-36

Displaying the terms in a row we get

x² – 6x + 6x – 36 = x² – 36

Example: Factor x² – 49

Solution: We notice that the square root of 49 is 7. Therefore we write

x² – 49 = (x + 7)(x – 7)

Difference of squares is easy to spot and factor if it’s plain. However, it may be “hidden” by a common factor:

Example: Factor 2x³ – 50x

Solution: We notice that 50x isn’t square rootable. However, we also notice that 2x can be taken out front as a common factor:

2x³ – 50x = 2x(x² – 25)

Now, we’re getting somewhere: we follow with

2x(x² – 25) = 2x(x + 5)(x – 5)

Removing the common factor of 2x allowed us to apply the difference of squares technique.

Have a nice day:)

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.