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Polynomials - Difference of squares

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

Problem Num : 1

From : AMC10

Type:

Section:Polynomials

Theme:
Adjustment# : 0

Difficulty: 1

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

Category Difference of squares

Analysis

Solution/Answer
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 $mathrm{(E)}$ .

Answer:

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