x^2-5/3 can be written as 3x^2-5

Question

[x-(underroot)5/3]*[x+(underoot)5/3]

 When this is simplified we get [x^2-5/3] 

can it be written as 3x^2-5???

Answer 1

Hi Shawez,

 

I think this is your question but honestly it's a bit difficult to discern so if my assumption is wrong, please let me know.

 

We begin with 

 

[x -√(5/3)] [x +√(5/3)]

 

Foil (first, outer, inner, last)  this just as you would any other set of factors.

 

x² + x√(5/3) - x√(5/3) - [√(5/3)]² 

 

The two x√(5/3) terms cancel, leaving us with 

 

x² - [√(5/3)]² 

 

x² - 5/3

 

3x²-5 ≠ x2 - 5/3

Rather,

3x²-5 = 3(x² - 5/3)