TRY IT:

Use the critter above to expand( x + 2 )^( 5 )

 


Let's use this new info to do some trickier problems.

Let's find the 13th term in the expansion of ( a + b )^( 15 )...  Without
pathetically trying to multiply it all out!  

          OK, think about it...

          The second variable... the b...

          The b guy starts at  b^( 0 )and goes up one each time...  So, at the
       13th term, it will be

b^( 12 )

No more thinking left to do now!

a^(  )b^( 12 )  ...  ( a + b )^( 15 )  ...  The exponents in the first equation have to add up to the exponent of the seond equation

 

a^( 3 ) b^( 12 )
 

Now, pop the coefficient:

( 15! / 3! 12! ) * a^( 3 ) * b^( 12 ) = 455a^( 3 )b^( 12 )