sat suite question viewer

Advanced Math / Equivalent expressions Difficulty: Hard

If a equals, c plus d, which of the following is equivalent to the expression x squared, minus c squared, minus 2 c d, minus d squared?

Back question 60 of 102 Next
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102

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.