Question

in the expression of (4r+s)^7 what is the coefficant in this term

Answer 1

Which term?

Answer 2

r^4 s^3

Answer 3

Are you familiar with the Binomial Theorem and Pascal's Triangle ?

Answer 4

a little

Answer 5

I suggest a little research on it because it comes in handy.

Remember that the r^4 term will also have a 4^4 term because 4 is already a coefficient of r.

Basically what it tells us is that the 4^4 * r^4 * s^3 term is the fourth term (counting backwards from the exponent 7, we get : 7, 6, 5, 4 ,totaling four terms.

The binomial coefficient then of the fourth term is:

\[\left(\begin{matrix}7 \\ 4\end{matrix}\right) = 35\]

Since we already have a 4^4 term, we multiply 4^4 * 35 = 8960

Thus the coefficient is 8960.

Some research for Binomial Theorem ( http://www.purplemath.com/modules/binomial.htm)