Factoring 28s^2 + 8st - 20t^2: A Simplified Explanation and Solution

[Rowah]

Homework Statement

$$28s^2 + 8st - 20t^2$$

The answer in the back of the book is 4(7s - 5t)(s + t)

2. The attempt at a solution

$$4(7s^2 + st + st - 5t^2)$$
$$4(7s^2 + st + st - 20t^2)$$
$$4(s(7s + t) + t(s - 20t))$$

I'm lost, can someone please help me?

Thanks in advance.

 

[robb_]

In your first attempt at the solution, why not combine the second and third terms inside the (), it might make things more obvious.

 

[Rowah]

Is there some trick to this that I am missing?

$$4(7s^2 + 2st - 5t^2)$$

 

[cristo]

Well, you could note that 2st=7st-5st, which makes your expression 4(7s²+7st-5st-5t²). Is this any easier to factorise?

 

[Rowah]

OHH OHH OHHHH OHHHHHH!

Oh my god, how could I be so blind? That t^2 at the end threw me off. I feel like such an idiot. Thanks a billion cristo and robb, and I apologize for wasting your time :)