Difference between revisions of "1950 AHSME Problems/Problem 16"
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== Problem== | == Problem== | ||
| − | The number of terms in the expansion of <math> [(a+3b)^{2}(a-3b)^{2}]^{ | + | The number of terms in the expansion of <math> [(a+3b)^{2}(a-3b)^{2}]^{4} </math> when simplified is: |
<math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> | <math> \textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8 </math> | ||
Revision as of 18:25, 23 August 2019
Problem
The number of terms in the expansion of ![$[(a+3b)^{2}(a-3b)^{2}]^{4}$](http://latex.artofproblemsolving.com/f/4/f/f4f1bc66f095186cd44c30f31f9d0f8e8cd7e7bf.png)
when simplified is:
Solution
Use properties of exponents to move the squares outside the brackets use difference of squares.
![\[[(a+3b)(a-3b)]^4 = (a^2-9b^2)^4\]](http://latex.artofproblemsolving.com/d/8/8/d88510de517abcc0d064612d89e7094e4470ec69.png)
Using the binomial theorem, we can see that the number of terms is 
See Also
| 1950 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 15 |
Followed by Problem 17 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
