ALGEBRA 1 FACTORING HELP!! -CALLING ALL SMART PPL-

[MagixAries]

Please help me with these Algebra 1 problems!! Please show how you did it and why becuz Im really bad at Algebra and needs step-by-step help! >.<"

Factor each Expression.
1) 100v^2 - 25w^2
2) 28c^2 + 140cd + 175d^2
3) x^2 + x + 1/4
4) 64t^2 - 192gh + 144h^2
5) 1/25k^2 + 6/5k + 9

PLEASE SHOW YOUR WORK & WHY U DID EACH STEP PLEASE!! IM REALLY CONFUSED IN THIS TRINOMIAL FACTORING STUFF! THANKS A WHOLE BUNCH!!

[Alen]

1) 100v^2 - 25w^2
> difference of squares
> (10v)^2-(5w)^2
> (10v-5w)(10v+5w)
2) 28c^2 + 140cd + 175d^2
> 7(4c^2+20cd+25d^2)
> 25 can only be the product of 5*5 or 1*25, getting 20cd is easier with 5*5 (2*(2*5))
> 7(2c+5d)^2
3) x^2 + x + 1/4
> (x+1/2)^2
4) 64t^2 - 192gh + 144h^2
> assuming that t=g (typo?), pretty evident that 64 = 8^2, -192 = 2*8*(-12) and (-12)^2=144
> (8t-12h)^2
5) 1/25k^2 + 6/5k + 9
> to make it easier, factor out 1/25
> 1/25(k^2+30k+225)
> pretty evident that 15^2=225 and 2*15 = 30
> 1/25 * (k+15)^2

You'll probably want to take a look at this: Vieta's formulas - Wikipedia, the free encyclopedia