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# Which of the following is equivalent to (a^100-b^100)/(a^50-b^50)

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Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) [#permalink]
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

$$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$

= $$\frac{(a^{50})^2 - (b^{50})^2}{a^{50}-b^{50}}$$

= $$\frac{(a^{50}+b^{50})(a^{50}-b^{50})}{a^{50}-b^{50}}$$

= $$a^{50}+b^{50}$$

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Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) [#permalink]
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Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) a^2+b^2
(B) a^2-b^2
(C) a^50+b^50
(D) a^50-b^50
(E) (ab)^2

Kudos for a correct solution.

To solve this we have to remember the basic formula : $$a^2 - b^2 = (a+b)(a-b)$$

Here the numerator $$a^{100}-b^{100}$$ Can be changed to $$(a^{50})^2 -(b^{50})^2$$

Clearly this can now be re written as $$({a}^{50}+{b}^{50})({a}^{50}-{{b}^{50})$$

Simplify this with the denominator whats left is $${a}^{50}+{b}^{50}$$ and thus the Answer is C
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Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) [#permalink]
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[(a^50 - b^50)(a^50 + b^50)] / (a^50 - b^50)

Answer is (a^50 + b^50) = C
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Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) [#permalink]
Bunuel wrote:
Which of the following is equivalent to $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ for all values of a and b for which the expression is defined?

(A) $$a^2+b^2$$

(B) $$a^2-b^2$$

(C) $$a^{50}+b^{50}$$

(D) $$a^{50}-b^{50}$$

(E) $$(ab)^2$$

Lets $$a^{50} = x$$ and $$b^{50} = y$$

Now $$\frac{{{a}^{100}}-{{b}^{100}}}{{{a}^{50}}-{{b}^{50}}}$$ = $$\frac{{{x}^{2}}-{{y}^{2}}}{x-y}$$ = $$\frac{(x+y) (x-y) }{ (x-y)}$$ = (x+Y)

= $$a^{50} + b^{50}$$

Ans C
Re: Which of the following is equivalent to (a^100-b^100)/(a^50-b^50) [#permalink]
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