Question which-

2.4 Equivalent Expressions - Simplifying polynomials
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Which of the following is equivalent to parenthesis, a, plus the fraction b over 2, close parenthesis, squared ?

A.

a, squared, plus the fraction b squared over 2

B.

a, squared, plus the fraction b squared over 4

C.

a, squared, plus the fraction a, times b, over 2, end fraction, plus the fraction b squared over 2

D.

a, squared, plus a, times b, plus the fraction b squared over 4

Which of the following is equivalent to ?

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 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.