Question

The polynomial 8x2 - 9 is a difference of squares. T/F?

Answer 1

8x^2-9**

Answer 2

I think true but people are saying false?

Answer 3

Difference of squares has the form \(a^2-b^2\)
Can you find a value for \(a\) and \(b\) to match your equation? Obviously, \(b=3\) is half of the job, what about for \(a^2 = 8x^2\)?

Answer 4

?? All I asked was "True or False"

Answer 5

Yes, and I'm trying to help you know the answer without asking us :-)

Answer 6

\[a^2=8x^2\]Can you solve that for \(a\)?

Answer 7

I'm going with false.

Answer 8

Take the square root of both sides:
\[\sqrt{a^2} = \sqrt{8x^2}\]Remember that \(\sqrt{a^2} = a\)
\[a = \sqrt{8}*\sqrt{x^2} = x\sqrt{8}\]
So we can see that it is TRUE, because \[(x\sqrt{8})^2-3^2 = 8x^2-9\]