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Equivalent expressions SAT question

Math · Advanced Math · Hard · Answer it here, explanation included.

Which of the following is equivalent to parenthesis, a, plus the fraction b over 2, close parenthesis, squared ?

ExplanationShow

Choice D is correct. The expression open parenthesis, a, plus the fraction b over 2, close parenthesis, squared can be rewritten as open parenthesis, a, plus the fraction b over 2, close parenthesis, times, open parenthesis, a, plus the fraction b over 2, close parenthesis. Using the distributive property, the expression yields open parenthesis, a, plus the fraction b over 2, close parenthesis, times, open parenthesis, a, plus the fraction b over 2, close parenthesis, equals, a, squared, plus the fraction with numerator a, b and denominator 2, end fraction, plus the fraction with numerator a, b and denominator 2, end fraction, plus the fraction b squared, over 4. Combining like terms gives a, squared, plus a, b, plus the fraction b squared over 4.

Choices A, B, and C are incorrect and may result from errors using the distributive property on the given expression or combining like terms.

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