Question

3. Identify the third term in the expansion of (7x – 2y)3.

Answer 1

So ummm, we can use `Pascal's Triangle` and start to expand out the binomial and just stop once we get to the 3rd term.

Or we can use the `Binomial Theorem` to jump right to the 3rd term.

Which method would make more sense to you? :o

Answer 2

pascals triangle

Answer 3

This line will give us the coefficients for a 3rd degree binomial.

Answer 4

So do you understand how this kind of works?
The exponents on the a's count down from 3 as we move to the right,
while the b's count upward, yes?
\[\Large (a+b)^3 \quad=\quad 1\cdot a^3b^0+3\cdot a^2b^1+3\cdot a^1b^2+1\cdot a^0b^3\]

Answer 5

So in our case, our a=7x, b=-2y

Answer 6

\[\large \left([7x]+[-2y]\right)^3=\\ \large 1\cdot[7x]^3[-2y]^0+3\cdot[7x]^2[-2y]^1+\color{orangered}{3\cdot[7x]^1[-2y]^2}+...\]

Answer 7

So there is our 3rd term, in orange.
I hope the square brackets aren't too confusing.

Answer 8

thank you so much