binomial theorem

[Pam L in Mid Tenn]

In what "course" is this usually taught? Algebra 2?

(I think I remember it from College Algebra back in "the dark ages".:D)

 

Thanks again!

[creekland]

In our high school we don't teach it at all. It's in our College Alg book, but we don't get that far. We stick with our local cc standards and syllabus, so they wouldn't cover it either.

 

In our earlier classes we explain how to multiply binomials (of course) and therefore, cover squares and cubics, but we never touch on the theorem itself.

 

Were you just asking how to do them without the theorem? If so, that's in Alg 1.

[Jane in NC]

The old Dolcianis have the Binomial Theorem at the end of Algebra II/Trig. It appears fairly early on in the subsequent text, Modern Introductory Analysis (what we would now call a Precalculus book).

 

So one could place the Binomial Theorem in either or both classes from my perspective.

[creekland]

I checked Lial's Pre-Calc here at home. It's very near the end in additional topics. Ditto that for my TT Pre-Calc book - it's in Additional Topics near the end.

 

In the College Alg book at school it was in Chapter 9, but our syllabus only goes through Chapter 7.

[Caroline]

I learned it in Algebra II. I teach it in Pre-Calculus, although I don't really think it is a standard there. I just like to teach it.

[Pam L in Mid Tenn]

Ok... thanks.

I'll consider this lesson an introduction and will not test over it.

 

It is taught in lesson 10 of MUS using a different formula than I remembered. My son understands and gets correct answers when he looks at Pascals Triangle but doesn't really "get" the forumla.

 

I'm considering supplementing with Tobey/Slater Intermediate Algebra and could not find the Binomial Theorem even introduced in that book.

 

Sometimes MUS seems to easy.... and sometimes it seems to hard!

Thanks,

Pam

[mom2bee]

Its taught in PreCalculus in my CC, but only by some teachers. I was never taught this, but friends in other classes with a different teacher were. Its in the back of our PreCalc book. The last section of the CH11 (CH12 is on limits...which no one does in PreCalc at my school.)

[regentrude]

Our math book covers it in Intermediate Algebra.

Lial Intermediate Algebra does too, in chapter 11.

[Running the race]

In Math U See, it is in Algebra 2 about 1/3 of the way through the course.

[Teachin'Mine]

In Saxon, it's covered in Advanced Math in Lesson 112. There are 125 lessons in that text.

[Kathy in Richmond]

The Binomial Theorem can be introduced at any time from algebra to college courses depending on the depth of the coverage.

 

After the student learns to multiply polynomials in algebra, you can have him look for patterns and 'discover' the theorem by multiplying out powers of (x + y):

 

(x + y)^2 = x^2 + 2xy + y^2

(x + y)^3 = x^3 + 3 x^2 y + 3 x y^2 + y^3

(x + y)^4 = x^4 + 4 x^3 y + 6 x^2 y^2 + 4 x y^3 + y^4

 

etc, and he'll see that the coefficients in the expansions match the numbers in the rows of Pascal's triangle:

 

....................1................

................1......1............

............1......2.......1.......

.........1.....3.......3.......1..

.....1......4......6.......4......1

 

That's a fun exercise and can be done even in algebra 1 if you'd like.

 

Writing out the Binomial Theorem in general for (x + y)^n for the nth power takes a little more sophistication, and isn't usually introduced till the end of the second year of algebra or precalculus.

 

Proving this theorem is yet another stage of difficulty. It can be done once the student learns about proofs by mathematical induction (not always a part of standard high school courses...see AoPS books if you want something like this :)). My dd had to prove it this way as an exercise at the beginning of her real analysis course in college.

[Tattarrattat]

I think AoPS introduces it in their Introduction to Counting and Probability book.