Question

Explain, in complete sentences, how you would expand (3x + 7y)4 using Pascal’s Triangle.

Answer 1

** (3x + 7y)^4

Answer 2

First write out pascals triangle up to at least 5 rows. Then expand as \[(3x)^4*(7y)^0+(3x)^3*(7y)^1+(3x)^2*(7y)^2+(3x)^1*(7y)^3+(3x)^0*(7y)^4\]. Simplify, then multiply the results by the coefficients found in the the 5th row of pascals triangle. We use the 5th row because it is in general the (n+1)st row where n is the order of the equation (in this case n=4). The 5th row is 1,4,6,4,1 which we multiply by the corresponding term in the expansion. i.e.
1(first term)+4(second term)+6(third term)+4(fourth term)+1(fifth term)