Question if-whi
If 
, which of the following is equivalent to the expression 
?
If , which of the following is equivalent to the expression ?
Hard-difficulty · SAT Math · Equivalent Expressions — Simplifying polynomials. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.
Answer explanation
Choice C is correct. Factoring –1 from the second, third, and fourth terms gives x2 – c2 – 2cd – d2 = x2 – (c2 + 2cd + d2). The expression c2 + 2cd + d2 is the expanded form of a perfect square: c2 + 2cd + d2 = (c + d)2. Therefore, x2 – (c2 + 2cd + d2) = x2 – (c + d)2. Since a = c + d, x2 – (c + d)2 = x2 – a2. Finally, because x2 – a2 is the difference of squares, it can be expanded as x2 – a2 = (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 x2 – a2. Choice D is incorrect and may be the result of incorrectly combining terms.
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