Binomial Theorem

Probability Level 2

How many terms are in the expansion of $\left [ \left ( 7r-9k \right )^{3} \left (7r+9k \right )^{3}\right ]^{4}$ , assuming that $r$ and $k$ are distinct variables?

12 13 11 10

1 solution

Aaron Tsai
May 10, 2016

$\left [ \left ( 7r-9k \right )^{3}\left ( 7r+9k \right )^{3} \right ]^{4}=\left [ (49r^{2}-81k^{2})^{3} \right ]^{4}=\left ( 49r^{2}-81k^{2} \right )^{12}$

Using the Binomial Expansion Theorem, we can see that the number of terms in this is also the same as the number of numbers in the 12th row of Pascal's Triangle, which is $12+1=\boxed{13}$ .

Binomial Theorem

1 solution

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