M01-12

Hello, mvrravikanth. I doubt you are still hanging around this forum, but your question is, and my thinking is that if you approached the problem in such a way, then other people probably have (or will), too. My post is an effort to clarify a matter or two. In your assessment of statement (1), the third line should have a plus sign before \(3p\)\(q^2\). However, you correctly factored out that \(-3pq\) in the next step, and your solution for statement (1) is quite interesting to me. Yes, since you know that \(p - q = 0\), you could substitute and end up answering the exact question that is being asked, \(p^3 - q^3 = 0\). It may not be the fastest way to solve the question, but I like the creativity.

In your assessment of statement (2), it is not quite clear what you mean by we will get \(p^3 + q^3\). That is, you get \(p^3 + q^3\) as part of an expanded distribution, but what about the other terms? I know from the other analysis that you know how to distribute binomials, and how to further distribute a binomial into a quadratic. Did you just decide that the \(p^3 + q^3\) part was enough to write off the sufficiency of the statement? Did you try numbers? I ask because I know from tutoring that a rookie mistake is to assume that a binomial raised to an exponent, for example \((p + q)^3\), is the same as distributing the power, \(p^3 + q^3\), and that is not correct.

- Andrew

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.