Factor completely and explain please...?

Question

49- 1/121s^2

&

s^2 - 1/16

Fractions are the absolute worst for me...

Answer 1

(7-1/11s)(7+1/11s)

(s-1/4)(s+1/4)

Answer 2

Take, for example, the second expression:
s^2 - 1/16

There are some clues here that point you to the solution. It's not really about fractions.
You have to recognize that this is the difference of squares.
When you have something like s^2 which is one s times itself FOLLOWED by a negative sign FOLLOWED by something else squared (look at 1/16 and you should see 1/4 times 1/4 or in other words, 1/4 squared), you have the difference of two squares.
The difference of two squares is always going to look like this, factored:
(a+6)(a-6)
(b+2)(b-2)
(c+9)(c-9)
That's the point of the examples you've been given to factor. They are both difference of two squares examples.
(s+1/4)(s-1/4) ----> s^2 - 1/16

Every algebra text will explain the difference of two squares when there's a factoring chapter so you can look in the index of your text book if you still don't understand.

Similarly, 49-1/121s^2 is the same kind of thing. It's been tricked up to look different but it is still a squared thing followed by a minus sign followed by another squared thing.
So (7+1/11s)(7-1/11s) is the answer to that. It assumes you're going to look at that 121 denominator and know that it is 11 times 11. And in every situation where there's a 1 in the numerator, 1 times 1 is 1 so you really only look at the denominator to get your answer!

Answer 3

Question 1
(7 - 1 / 11s) (7 + 1 / 11s)
Check
7 x 7 = 49
7 / 11s - 7 / 11s - 0
(- 1 / 11s) (1 / 11s) = - 1 / 121s²

Question 2
(s - 1/4) (s + 1/4)
Check
s² + 1/4 s - 1 / 4 s - 1 / 16 = s² - 1 / 16

Answer 4

a²-b² all of which factor into
(a+b)(a-b)

Note 1/121=(1/11)² and 1/16 = (1/4)²

With that information you should be able to do these yourself.... or you can wait for somebody else to do them for you. It depends on whether or not you want to learn the stuff. You might use this information and do them yourself... and then check your answers against those posted.