Quandaries and Queries
  


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 r2n - 5 s4n is that there is a common factor of 5. Take out this common factor to get 5(9 r2n - s4n)

Now I see squares. 9 = 32, r2n = (rn)2 and s4n = (s2n)2. Thus, since

9 r2n = (3 rn)2 and s4n = (s2n)2 I see he expression 5(9 r2n - s4n) as 5(a2 - b2) with a = 3 rn and b = s2n

But

a2 - b2 = (a - b)( a + b) and hence 5(9 r2n - s4n) = 5(3 rn - sn)(3 rn + sn)

I hope this helps,
Penny


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