If , which of the following is equivalent to the expression ?

Question

Accepted Answer

Choice C is correct. Factoring -1 from the second, third, and fourth terms gives x 2 - c 2 - 2 cd - d 2 = x 2 - ( c 2 + 2 cd + d 2 ). The expression c 2 + 2 cd + d 2 is the expanded form of a perfect square: c 2 + 2 cd + d 2 = ( c + d ) 2 . Therefore, x 2 - ( c 2 + 2 cd + d 2 ) = x 2 - ( c + d ) 2 . Since a = c + d , x 2 - ( c + d ) 2 = x 2 - a 2 . Finally, because x 2 - a 2 is the difference of squares, it can be expanded as x 2 - a 2 = ( x + a )( x - a ). Choices A and B are incorrect and may be the result of making an error in factoring the difference of squares x 2 - a 2 . Choice D is incorrect and may be the result of incorrectly combining terms.

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