Question

A student is attempting to simplify the expression below. Sample mathematical work is shown. Which statement best applies to the sample mathematical work? Given 2003-01-05-00-00_files/i0330000.jpg, I first apply the distributive property, which yields the expression xy + yx + x – 3x – 3y. I can then collect like terms: since x – 3x = –2x, I have the expression xy + yx – 2x – 3y as my final answer. A. The student failed to properly apply the distributive property. B. The student collected two or more terms that were not like terms. C. The student failed to collect all like terms. D. The mathematical work shown above is correct.

Answer 1

The answer would be letter C. The student failed to collect all like terms.

Specifically, the student failed to notice that the terms xy and yx are like terms. In algebra, when terms are multiplied, the order of the variables do not matter; they are similar. Thus, the simplified expression should have been 2xy - 2x -3y.