In the 1st post of this series I made a case for teaching factoring. In the 2nd I described multiplying polynomials by “double distribution” (no FOIL!) so that:

$(3x - 4y)(x + 6y) =$
$3x(x + 6y) - 4y(x + 6y)$

So we do Greatest Common Factor work and arrive at 3 examples like these:

 ax + 5x a@# + 5@# a?%?%? + 5?%?%? x(a + 5) @#(a + 5) ?%?%?(a + 5)

Then this:
a(y + z) + 5(y + z)
(y + z)(a + 5)

(I use squiggles for the intermediate steps. Ach, this is nice. We compare it to our double distribution. But we need one more step back, first.)

an – 5n + ax – 5x
n(a – 5) + x(a – 5)
(a – 5)(n + x)

Now we see the double distribution, moving from bottom to top. Note, the first step is to factor out the GCF “pairwise,” which I emphasize orally and by underlining the pairs within the expression.

One day for just this, nothing harder than:

$6b^2 - 9bk + 10bc - 15ck$
And trinomials come the next day (and in my next post)

1. September 10, 2007 pm30 1:52 pm 1:52 pm

I’m totally with you on this one.