## Friday, March 8, 2013

### Math problems of the week: factoring in UCMP vs. 1900s algebra

I. The final page of factoring problems in the University of Chicago Math Project Algebra textbook (Chapter 12 of 13 chapters) [click to enlarge]:

II. The final page of factoring problems in Wentworth's New School Algebra textbook (Chapter 7 of 17 chapters) [click to enlarge]:

III. Extra Credit

What do the University of Chicago Math Project students miss out on by not having problems as challenging as problem #121 above?

What did Wentworth's students miss out on by not having SPUR Objectives, where, once again:

#### 1 comment:

Anonymous said...

Boy, I really got off track into the weeds with that last one until I saw the trick.

x^4 - 2abx^2 - a^4 - a^2b^2 - b^4
= (x^4 - 2abx^2 + a^2b^2) - (a^4 + 2a^2b^2 + b^4)
= (x^2 - ab)^2 - (a^2 + b^2)^2

But m^2 - n^2 = (m + n)(m - n), so we have:

= [(x^2 - ab) + (a^2 + b^2)][(x^2 - ab) - (a^2 + b^2)]
= (x^2 - ab + a^2 + b^2)(x^2 - ab - a^2 - b^2)