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About Scott A Wilson
Expertise
I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math.

Experience
Experience in the area; I have tutored people in the above areas of mathematics for almost two years in AllExperts.com. I have tutored people here and there in mathematics ever since I received a BS degree almost 25 years ago. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors. Past/Present Clients: College Students at Oregon State University, various math people since college, over 2,000 people ion the PC from the US and rest the world.

Publications
My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

Education/Credentials
Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

Awards and Honors
I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes, I was first. I graduated with well over 50 credits in upper division mathematics.

Past/Present Clients
My clients have been students at OSU, people nearby, and friends with math questions, and several people every day on the PC. Just like you.

You are here: Experts > Science > Mathematics > Advanced Math > Simplifying with Pascal's Triangle

Advanced Math - Simplifying with Pascal's Triangle

Expert: Scott A Wilson - 11/2/2009

Question
Can you please help me simplify these products using Pascal's Triangle?
(x+1)^5
(x+1)^6
(x+1)^7
(x+1)^10

Answer
Pascal's Triangle:
Each row is found by the sum of two elements above it.
On the edge, it is always 1.
5   :   1   5   10   10   5   1
6   :   1   6   15   20   15   6   1
7   :   1   7   21   35   35   21   7   1
10   :   1   10   45   120   210   252   210   120   45   10   1

Each element starts with 1, the next is x, the next is x², the next is x³, etc.

For example, x^5 would use 1 5 10 10 5 1 as the coefficients.
This would be be 1x^5 + 5x^4 + 10x^3 + 10x^2 + 5x + 1.
Note the 1 can be left out in front of x^5, it was just put there to show where it came from.

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