How do I find the 3rd term of (x + 3y)11?

Question

How do I find the 3rd term of (x + 3y)11?

Answer 1

You need to look at the 12th line of pascal's triangle, which tells you that the 1st - 3rd terms of (a + b)^11 are

a^11 + 11a^10b + 55a^9b^2 + ...

Substituting x and 3y for a and b we have the first three terms:

x^11 + 11x^10(3y) + 55x^9(9y^2) + ...

x^11 + 33x^10y + 495x^9y^2 + ...

The answer is 495x^9y^2

Answer 2

(x+3y)^11   ???

Use Pascal's Triangle

*************1****1             1st power

***********1****2****1              2nd power

********1****3****3****1              3rd power

******1****4****6****4****1

Continue the pattern you see above (add the two numbers above) to the 11th power.

The third term in that row will be the coefficient (55) to be multiplied by (1x)^9 (3y)^2

(55)(1x)^9(3y)^2  =  455(x^9)(y^2)

This is known as binomial expansion.

Answer 3

X is the first term,

+3y is the second,

and 11 is the third.

Good Luck!