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Expert: Robi Bhattacharjee - 1/22/2009


Question
my son was asked to factor x^4^m - y^4^n he has looked in his book and we have tried several ways to work it but we just come back to the problem itself? How do we work this?

Answer
Hi Terry,

x^4^m can be written as (x^a)^4 for some a. Take an example. let m = 3. Then x^64 = (x^16)^4. Similarly, y^4^n can be written as (y^b)^4. Now note that a = 4^(m-1) and b=4^(n-1).

So let us say that x^a = p and y^b = q.

Then the problem becomes p^4 - q^4 = (p-q)(p+q)(p^2+q^2).

So that is the factoring where p = x^a and q = y^b and a = 4^(m-1) and b = 4^(n-1).

I hope this helps,
Robi

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Robi Bhattacharjee

Expertise

I can answer a variety of questions on mathematics. Questions on trigonometry, calculus(preferably single variable), algebra, geometry, and number theory will be answered. I cannot answer questions on abstract branches of mathematics such as group theory. I also cannot answer questions on statistics. In number theory, I can answer questions on congruences, prime numbers, units, functions, and the riemann-zeta function.

Experience

I have studied advanced math my entire life. I started calculus in sixth grade. I have attended numerous math competitions and I am attending math organizations such as the San-Diego math circle. Also, this year I have been invited to the USAMO which is a prestigious math competition (Every year the USAMO invites 500 students from across the USA to participate in this competition. The top 6 go to represent the USA in the International Math Olympiad).

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I am in the San Diego Math Circle

Education/Credentials
I am entering high school and have received a perfect score and the STAR test 5 times in a row. I also have gotten recognitions in the AMC 10, AIME, Math Counts, and ARML. Additionally, I have won the San Diego Math Olimpiad twice in a row.

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