Question which-

2.4 Equivalent Expressions - Simplifying polynomials
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open parenthesis, 2 x cubed, plus 3 x, close parenthesis, times, open parenthesis, x cubed, minus 2 x, close parenthesis

Which of the following is equivalent to the expression above?

A.

x cubed, plus 5 x

B.

3 x cubed, plus x

C.

2 x to the sixth power, minus x to the fourth power, minus 6 x squared

D.

3 x to the sixth power, minus x to the fourth power, minus 6 x squared

Which of the following is equivalent to the expression above?

Medium-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 C is correct. Using the distributive property to multiply the terms in the parentheses yields open parenthesis, 2 x cubed, times x cubed, close parenthesis, plus, open parenthesis, 2 x cubed, times negative 2 x, close parenthesis, plus, open parenthesis, 3 x times x cubed, close parenthesis, plus, open parenthesis, 3 x times negative 2 x, close parenthesis, which is equivalent to 2 x to the sixth power minus 4 x to the fourth power, plus 3 x to the fourth power, minus 6 x squared. Combining like terms results in  2 x to the sixth power minus x to the fourth power, minus 6 x squared.

Choices A and D are incorrect and may result from conceptual errors when multiplying the terms in the given expression. Choice B is incorrect and may result from adding, instead of multiplying, open parenthesis, 2 x cubed, plus 3 x, close parenthesis and open parenthesis, x cubed, minus 2 x, close parenthesis.