A Factor of Cubes

factor of cubes

I was trying to help my niece with her math homework the other night.  She has just started her first year of community college (I am very proud to say) and is struggling with the factoring of cubes.

My weak efforts at assistance were necessarily over the phone, as my niece lives in northern California, more than 600 miles from our small-town abode out in the Sonoran Desert.  I would much rather have been sitting on the couch next to her, poring over her textbook and trying out tentative solutions on scrap paper.

As if the challenges of long-distance math aren’t enough, it has been decades since I last studied algebra.  I have no confidence at all in my memory’s accuracy regarding x and y, exponents and coefficients.  And in any event, I have no clue as to how they’re teaching algebra these days.  I recall my parents bemoaning the “new math” back in the day; who knows what’s in vogue in the twenty-first century.

“There are three main methods of factoring,” I began explaining to my niece.

“Wait,” she said, “let me get a piece of paper to write this down,” as if I were about to impart some type of profound wisdom that must be preserved for the ages.

I proceeded to explain a little about the greatest common factor, the difference of squares and the quadratic equation.  I soon discovered that knowing the theory is very nice, but of little value when faced with a flummoxing string of constants and variables.

I suggested that my niece notice the cubed exponent and then notice that all of the terms in the expression are perfect cubes.  And then I became stuck.  All I could do was urge my niece to try to remember the lecture, go over her notes again, and take the approach recommended by her teacher.  The problem, she related, is that the professor has more than a bit of an attitude, insisting that the material covered at the beginning of the semester is solely in the nature of review, and that he expects his students to already know how to handle factoring.

After I hung up, I was seized by regret that I couldn’t be of more help with my niece’s math problem.  And that’s when I remembered that we’re not back in the seventies anymore, where the best you could do was call a friend in the class to see if perhaps he or she had already figured out how to calculate the answer.  No, indeed.  Today we have the internet.  In a minute or two I had performed a quick Google search and found the holy grail.

Calling back my niece, I revealed my online discovery that factoring cubes has to be done by formula, albeit a formula that I had never seen in my life.  She dutifully wrote down the additive and subtractive formulas that I read off my screen, after which I explained how to plug in the terms of her problem to the variables of the formula.  Sure enough, we came up with the answer listed in the back of her textbook!

Over the long distance phone lines, I could feel a light go on.  Yes, my niece admitted, the professor had mentioned this very formula, but not until the very end of the session, after the class had flailed helplessly through similar problems for most of the hour.  She thanked me profusely and I signed off with a “Yay, Google!”

Alas, my nieces and nephews have all reached the age when I am forced to step off my pedestal, relinquishing that lofty perch in favor of admitting that I am not as smart as they think I am.  As fascinating as I find mathematics, it has never been my academic strong suit.  I would be a far more valuable resource as a proofreader of my niece’s term papers than as a tutor fit to plumb the mysteries of equations.  Ask me the meaning of a word, and I will likely provide a mini-lecture on its derivation from Latin or Greek or Hebrew, while pointing out its root and suffix and comparing it to similar words in our own language or in French or Spanish.  But when it comes to things like algebra, trigonometry and (heaven help us) calculus, I’ll just have to key the problem into a search engine and hope for the best.

In other words, dear niece, I will just have to learn right along with you.  And maybe that won’t be so bad after all.