Difference between revisions of "1950 AHSME Problems/Problem 16"

Revision as of 07:32, 29 April 2012

The number of terms in the expansion of $[(a+3b)^{2}(a-3b)^{2}]^{2}$ when simplified is:

$\textbf{(A)}\ 4\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 6\qquad\textbf{(D)}\ 7\qquad\textbf{(E)}\ 8$

Use properties of exponents to move the squares outside the brackets use difference of squares.

$[(a+3b)(a-3b)]^4 = (a^2-9b^2)^4$

Using the binomial theorem, we can see that the number of terms is $\boxed{\mathrm{(B)}\ 5.}$

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

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 ==See Also==
-{{AHSME box|year=1950|num-b=15|num-a=17}}
+{{AHSME 50p box|year=1950|num-b=15|num-a=17}}
 [[Category:Introductory Algebra Problems]]