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Difference of squares : 1

Factorization and modification : 4

Factorization and more : 6

The Quotient-Remainder Theorem : 3


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Polynomials - Difference of squares

SOURCE:COMPETITION
Number of Problems: 1.
FOR PRINT ::: (Book)

Problem Num : 1
Type:
Topic:Polynomials 

Adjustment# : 0
Difficulty: 1
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The fraction frac{left(3^{2008} ight)^2-left(3^{2006} ight)^2}{left(3^{2007} ight)^2-left(3^{2005} ight)^2} simplifies to which of the following?

mathrm{(A)} 1qquadmathrm{(B)} frac{9}{4}qquadmathrm{(C)} 3qquadmathrm{(D)} frac{9}{2}qquadmathrm{(E)} 9

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Category Difference of squares
Analysis
Solution/Hint

Notice that 9 can be factored out of the numerator: frac{left(3^{2008} ight)^2-left(3^{2006} ight)^2}{left(3^{2007} ight)^2-left(3^{2005} ight)^2}=frac{9left(3^{2007}... Thus, the expression is equal to 9, and the answer is mathrm{(E)}.