Who is asking: Student
Level: Middle
Question:
Hi I was hoping you could help me with 2-3 problems in math.
Directions: Factor assuming that n is a positive #
Problem: (I will give it to you in words beacuse I don't know how to do exponents on the computer.)
Forty-five r to the 2n power minus five s to the 4n power.
I was hoping you could walk me through it not just give me the answer.
Thanks
Susie
Hi Susie,
The first thing I see when I look at
45 r^{2n} - 5 s^{4n}
is that there is a common factor of 5. Take out this common factor to get
5(9 r^{2n} - s^{4n})
Now I see squares. 9 = 3^{2}, r^{2n} = (r^{n})^{2} and s^{4n} = (s^{2n})^{2}. Thus, since
9 r^{2n} = (3 r^{n})^{2} and s^{4n} = (s^{2n})^{2}
I see he expression
5(9 r^{2n} - s^{4n})
as
5(a^{2} - b^{2})
with a = 3 r^{n} and b = s^{2n}
But
a^{2} - b^{2} = (a - b)( a + b)
and hence
5(9 r^{2n} - s^{4n}) = 5(3 r^{n} - s^{n})(3 r^{n} + s^{n})
I hope this helps,
Penny