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Advanced Math / Equivalent expressions Difficulty: Hard

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

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Explanation

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.