Binomial Expansion Using Pascal’s Triangle

Binomial Expansion Using Pascal’s Triangle

As an online math tutor, I love teaching my students helpful shortcuts! Algebra 2 and Precalculus students, this one is for you. Let’s learn a binomial expansion shortcut. Let’s say we want to expand (x+2)^3.

Without knowing a shortcut, we would start out by first writing this as (x+2)(x+2)(x+2). Then we could FOIL the first two terms.

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

Which gets us closer, but now we need to multiply these together (by multiplying everything in the first polynomial by everything in the second polynomial).

=(x^2+4x+4)(x+2)
=(x^3+2x^2+4x^2+8x+4x+8)
=(x^3+6x^2+12x+8)

Phew, we’re done. But what if we wanted to expand a binomial that has an exponent of 4 or 5? Multiplying all of those terms together can really make your head start spinning.

Luckily, there’s an easier way. We can use Pascal’s Triangle to expand binomials. Check out my video for four examples of using Pascal’s triangle to expand binomials.

-Katie, the online math tutor

Polynomial Division and Benefits of Online Tutoring

Polynomial Division and the Benefits of Online Tutoring

A precalculus student recently asked me if we could work on polynomial division.

“Of course!” I said. “Long division or synthetic division?”

She replied, “Oh, we’re learning the reverse tabular method. Can we do that?”

The reverse tabular method? I had never heard of this, but with a quick google search I learned a new method of dividing polynomials, which I want to share with you all today!

This is something I love about online tutoring: access to the internet provides so many resources. These are helpful in many scenarios, and especially when students bring some of that “new math” that is being taught in schools today. I’m able to quickly see examples of what they are talking about and teach what they are learning in school.

Check out the video below or on YouTube, and let me know if you have any questions, or if you’ve ever used this tabular method yourself. If you’re looking for one-on-one math help, head over here.

And let me know what topic you’d like for me to cover in my next video! I’m always looking for recommendations.

– Katie, the online math tutor