Question

factor p^4-1

Answer 1

this is going to be a difference of two squares problem. Do you know the formula for the difference of 2 squares?

Answer 2

i will if i see it..

Answer 3

this one is a bit nasty
(p-1)(p-1)(p^2+1)

Answer 4

\[a^2-b^2 = (a+b)(a-b)\]
look familiar?

Answer 5

it looks familiar but i do not remember how to do it

Answer 6

alright, step by step :)
first, lets rewrite the question to look like a difference of two squares:
\[p^4-1 \Rightarrow (p^2)^2-1^2\]

Answer 7

now lets just follow the formula:
\[a^2-b^2=(a+b)(a-b)\]
\[(p^2)^2-1^2 = (p^2+1)(p^2-1)\]

Answer 8

is that the final answer now? easier then it looks lol

Answer 9

but looking at that last term, there seems to be another difference of two squares O.o:
\[p^2-1 \Rightarrow p^2-1^2\]
so using the formula again:
\[a^2-b^2 = (a+b)(a-b)\]
\[p^2-1^2 = (p+1)(p-1)\]
so then we put everything together for the final answer:
\[(p^2+1)(p-1)(p+1)\]

Answer 10

ohh okay, can u help me with another

Answer 11

(:

Answer 12

sure :)

Answer 13

okay 6Y^2-54 factor

Answer 14

hmm...it doesnt look like a difference of two squares right away....maybe if we factor a 6 out of both terms?
\[6y^2-54 \Rightarrow 6(y^2-9)\]

Answer 15

and then break that down again?

Answer 16

yes :) do you see how you can break down that \[y^2-9\]
?

Answer 17

remember, you want things to look like:
\[a^2-b^2\]

Answer 18

its fine if you dont see it right away, it just takes practice :) what you want to do, it rewrite it like:
\[y^2-9 \Rightarrow y^2-3^2\]
Then you are in the perfect position to use the formula:
\[a^2-b^2 = (a+b)(a-b)\]
\[y^2-3^2 = (y+3)(y-3)\]
So the final answer would be:
\[6(y+3)(y-3)\]

Answer 19

ohhh !!! i see it now !! thanks