GRE Sample Test 5 Quantitative Reasoning 1

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Question : 9 of 20

Marks: +1, -0

4a^2 − 4b^2

is equivalent to which of the following?

(2a − 2b)(2a − 2b)
(4a − 4b)(4a − 4b)
(2a + 2b)(2a − 2b)
(2a + 2b)(a − b)
(4a + 2b)(4a − 2b)

Solution:

The expression in the question is in the form of

x^2 − y^2

, where

4a^2

corresponds to

x^2

and

4b^2

corresponds to

y^2

. Since

x^2 − y^2

factors to (x + y) (x − y),

4a^2 − 4b^2

factors to

(2a)^2 − (2b)^2

= (2a + 2b) (2a − 2b).

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