factor: 49x^2-36

Question

factor: 49x^2-36

anonymous · Answer

what is common between the 49x^2 and 36?

mathmale · Answer

Hello, Taylor!  Have you noticed that both 49x^2 and 36 are perfect squares?

Why not re-write your expression as (a)^2-b^2, the difference of two squares?

What next?  Does "difference of two squares" ring a bell for you?

anonymous · Answer

wouldn't the greatest common be 1?

anonymous · Answer

this is a difference of squares.

anonymous · Answer

i'm lost  :/

anonymous · Answer

what is the square root of 49? what is the square root of 36? both terms have square root?

mathmale · Answer

Taylor:  You're right.  Aside from that factor 1, and the fact that both 49x^2 and 36 are both squares, the two terms have nothing in common!

So again, I ask you:  Where have you heard "difference of two squares" before, and is there a special way in which to factor the "difference of two squares?"

anonymous · Answer

7 and 6

mathmale · Answer

Taylor:  You're on the right track.  But what about that x^2?

Hint:  Factor (or find the square root of)  49 x^2.

mathmale · Answer

$$\sqrt{49x^2}=?$$

anonymous · Answer

Okay now you know squareroot of 49 is 7 and 36 is 6... how about x^2?

mathmale · Answer

$$\sqrt{49x^2}=\sqrt{49}*\sqrt{x^2}=?$$

anonymous · Answer

(7x+6)(7x-6) ...?

mathmale · Answer

That's great!  Perfect!  Done!  Any questions about this procedure?

anonymous · Answer

nice job @taylorbeck16 ! You are correct!

mathmale · Answer

:)

anonymous · Answer

thanks @hello1213 and @mathmale

mathmale · Answer

Very happy that you're on OpenStudy.