Can somebody please help me with a few Pascal's Triangle questions?

1. Expand (x + 3)6 using Pascal’s Triangle. (2 points)
2. Expand (4x – 3y)4 using Pascal’s Triangle. (2 points)
3.Identify the third term in the expansion of (7x – 2y)3. (2 points)
4. Research the history of Pascal’s Triangle. Write a paragraph or two about its history, its uses, and patterns that may be found within it. Be sure to use quotations when necessary and cite all sources used in your research. (4 points)

Question

Can somebody please help me with a few Pascal's Triangle questions?

1. Expand (x + 3)6 using Pascal’s Triangle. (2 points)
2. Expand (4x – 3y)4 using Pascal’s Triangle. (2 points)
3.Identify the third term in the expansion of (7x – 2y)3. (2 points)
4. Research the history of Pascal’s Triangle. Write a paragraph or two about its history, its uses, and patterns that may be found within it. Be sure to use quotations when necessary and cite all sources used in your research. (4 points)

anonymous · Answer

@amistre64

agent0smith · Answer

https://upload.wikimedia.org/wikipedia/commons/thumb/f/f6/Pascal's_triangle_5.svg/250px-Pascal's_triangle_5.svg.png n=0 is the top row, you want n=6. http://www.mathwarehouse.com/algebra/polynomial/pascals-triangle.php

anonymous · Answer

I don''t understand... I'm really bad at this...

agent0smith · Answer

Find the row where n=6 (count from 0 from the first row in this pic http://daugerresearch.com/vault/PascalsTriangle.gif and it'll be the last) $$\LARGE x^6 \times 3^0 + x^5 \times 3^1 + x^4 \times 3^2 + ...$$ notice a pattern? pay attention to the powers on x and 3. Read this too: http://www.math10.com/en/algebra/probabilities/binomial-theorem/binomial-theorem.html

agent0smith · Answer

$$\LARGE x^6 \times 3^0 + x^5 \times 3^1 + x^4 \times 3^2 +  ...$$ Note that I left out the coefficients here, for you to find what they are.