Factoring

[Mackenzie25]

I just got my list of summer assignments to review before my calculus class and I'm kind of drawing a complete and utter blank on how to solve these problems(although I have this feeling they're pretty simple!). Any help would be wonderful, I just want to learn the basic idea of how to solve them so I can finish up all four of the problems below.
On the first problem, I've included my work, with my final answer, but when I entered it in on my assignment, it told me I had the wrong answer... :?
Thanks in advance!

1. 3w[sup:14sad7yy]2[/sup:14sad7yy]-147
factor out 3
3(w[sup:14sad7yy]2[/sup:14sad7yy]-49)

2. 144y[sup:14sad7yy]4[/sup:14sad7yy]-49

3. 9-100y[sup:14sad7yy]2[/sup:14sad7yy]

4. 36-w[sup:14sad7yy]2[/sup:14sad7yy]

 

[soroban]

Hello, Mackenzie25!


These are all of the same form: the difference of squares.

You should be familiar with this identity: .\(\displaystyle a^2 - b^2 \:=\a-b)(a+b)\)

I'll do the first one . . .

\(\displaystyle [1]\;\;3w^2 -147\)

What you did was correct . . .

\(\displaystyle \text{Factor out 3: }\;\;3\cdot\!\!\!\underbrace{\left(w^2 - 49\right)}_{\text{diff. of squares}}\)
. . . . . . . .\(\displaystyle =\;3\overbrace{(w-7)(w+7)}\)

 

[Deleted member 4993]

I just got my list of summer assignments to review before my calculus class and I'm kind of drawing a complete and utter blank on how to solve these problems(although I have this feeling they're pretty simple!). Any help would be wonderful, I just want to learn the basic idea of how to solve them so I can finish up all four of the problems below.
On the first problem, I've included my work, with my final answer, but when I entered it in on my assignment, it told me I had the wrong answer... :?
Thanks in advance!

1. 3w[sup:3t8owhs2]2[/sup:3t8owhs2]-147
factor out 3
3(w[sup:3t8owhs2]2[/sup:3t8owhs2]-49)

2. 144y[sup:3t8owhs2]4[/sup:3t8owhs2]-49

Hint:

= (12y[sup:3t8owhs2]2[/sup:3t8owhs2])[sup:3t8owhs2]2[/sup:3t8owhs2] - 7[sup:3t8owhs2]2[/sup:3t8owhs2]

3. 9-100y[sup:3t8owhs2]2[/sup:3t8owhs2]

Hint:

= (3)[sup:3t8owhs2]2[/sup:3t8owhs2] - (10y)[sup:3t8owhs2]2[/sup:3t8owhs2]

4. 36-w[sup:3t8owhs2]2[/sup:3t8owhs2]

Hint:

= (6)[sup:3t8owhs2]2[/sup:3t8owhs2] - (w)[sup:3t8owhs2]2[/sup:3t8owhs2]