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Test
Math
Domain
Advanced Math
Skill
Equivalent expressions
Difficulty
Medium
ID: cc776a04
Modded SAT Question Bank by Abdullah Mallik

Which of the following is an equivalent form of open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, squared, minus, open parenthesis, 5 point 2, x squared, minus 6 point 4, close parenthesis ?

  1. negative 2 point 2, x squared, plus 1 point 6
  2. negative 2 point 2, x squared, plus 11 point 2
  3. negative 2 point 95, x squared, minus 7 point 2 x, plus 12 point 16
  4. negative 2 point 95, x squared, minus 7 point 2 x, plus 0 point 64
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Correct Answer: C
Rationale

Choice C is correct. The first expression open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, squared can be rewritten as open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, times, open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis . Applying the distributive property to this product yields open parenthesis, 2 point 2 5, x squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, close parenthesis, minus, open parenthesis, 5 point 2, x squared, minus 6 point 4, close parenthesis . This difference can be rewritten as open parenthesis, 2 point 2 5, x squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, close parenthesis, plus, negative 1 times, open parenthesis, 5 point 2 x squared, minus 6 point 4, close parenthesis . Distributing the factor of negative 1 through the second expression yields 2 point 2 5 x, squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, minus 5 point 2, x squared, plus 6 point 4 . Regrouping like terms, the expression becomes open parenthesis, 2 point 2 5, x squared, minus 5 point 2, x squared, close parenthesis, plus, open parenthesis, negative 3 point 6 x minus 3 point 6 x, close parenthesis, plus, open parenthesis, 5 point 7 6 plus 6 point 4, close parenthesis . Combining like terms yields negative 2 point 9 5, x squared, minus 7 point 2 x, plus 12 point 1 6 .

Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.

Question Difficulty: Medium
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