Question

Hey guys. I used the grouping method to factor the function 9x^2-24x+16 and got (3x-4)^2. Is there another way to factor this? Fan/medal for help. :)

Answer 1

Here is another method :O\[\Large 9x^2-24x+16 \quad=\quad (3x)^2-2(3\cdot4)x+4^2\]

Recall how a perfect square binomial expands:\[\Large (a-b)^2 \quad=\quad a^2-2(a\cdot b)+b^2\]If we throw an x in the mix, it looks like:\[\Large (ax-b)^2 \quad=\quad a^2x-2(a\cdot b)x+b^2\]

Answer 2

So in our problem, it looks like we have ax=3x, b=4, right? :x
Lemme know if that method is too confusing :3

Answer 3

Bahh that first term should be a^2x^2.. typo +_+

Answer 4

I can't see the first answer you gave.

Answer 5

It says "math processing error"

Answer 6

Hmm weird D: are you using internet explorer?

Answer 7

Mozilla Firefox.

Answer 8

Hmm the fox shouldn't give you trouble D:
Try reloading the page maybe? :x

Answer 9

I did. I see it now. :)
So basically another method is expanding the trinomial?

Answer 10

I guess the way I would explain it is umm..
I wrote the factors in a way so that we could recognize that it's a `perfect square binomial`.

If it wasn't a perfect square, it would factor into something like... (3x-4)(3x+2) or something like that, where the brackets are not the same.

But ours factored down to (3x-4)(3x-4) which is the same as (3x-4)^2.
Not sure if that's easier than grouping.. just something to think about maybe :o

Answer 11

Well thank you. :)
I really appreciate it.

Answer 12

Is there a name for what you did or no?

Answer 13

Also, I think my question says it has to be the same factors, how would you find it that way?

Answer 14

ummmmmmm :x

Answer 15

Yes our factors turned out to be the same: (3x-4) and the other one is (3x-4), so that's good.

A name for it? D: Ummmmmmmm
I think if you google/youtube `Factoring Perfect Square Trinomials` you can find some good info on solving these.

Answer 16

So if you were to simplify what you gave me, it ends up as (3x+4)(3x-4).

Answer 17

what i gave you..? D:

Answer 18

The expansion..
(3x)^2-2(3x4)+4^2

Answer 19

\[\Large 9x^2-24x+16 \quad=\quad (\color{royalblue}{3x})^2-2(3\cdot4)x+\color{orangered}{4}^2\]
It's the thing you started with, I just wrote it a little different looking :o\[\Large =(\color{royalblue}{3x}-\color{orangered}{4})^2\]

Answer 20

You already figured this out by grouping, I was just trying to show you another method :D not a different problem.

Answer 21

Thank you. :)