Question

I am taking an online course for algebra 2 honors. I need help with some questions regarding Pascal's triangle and binomial expansion. I have 2 of them and I will need to see how its set up, the work to solve the problem, and the solution.

1) (x+3)^6
2) (4x-3y)^4

Now I also have one more question but it is a bit different.

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

Please help! I would appreciate if someone could help me right now and stay until I get it.

Answer 1

let us poke the 1st one

any ideas on the first term in \((x+3)^6\) ?

Answer 2

keep in mind that the exponents are the simplest part

the left-side term starts at "maximum" or in this case, 6, and gradually goes down to 0
from term to term, so \(\bf x^6, x^5, x^4, x^3, x^2, x^1, x^0\)

the right-side term, starts at "minimum", or 0, and gradually increases to "maximum", in this case 6 so \(\bf 3^0, 3^1, 3^2, 3^3, 3^4, 3^5, 3^6\)

the only part really that requires some fiddling is the coefficients

Answer 3

so... what do you think would be the 1st term for \((x+3)^6\quad ?\)

Answer 4

well... I read that, yes :) also read about the binomial theorem
so I figured he/she is using either to get the binomial expanded

Answer 5

It helps me to draw a picture, like this