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Advanced Math / Equivalent expressions Difficulty: Medium

open parenthesis, x minus 11 y, close parenthesis, times, open parenthesis, 2 x minus 3 y, close parenthesis, minus, 12 y, times, open parenthesis, negative 2 x, plus 3 y, close parenthesis

Which of the following is equivalent to the expression above?

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Explanation

Choice B is correct. Expanding all terms yields (x – 11y)(2x – 3y) – 12y(–2x + 3y), which is equivalent to 2x2 – 22xy – 3xy + 33y2 + 24xy – 36y2. Combining like terms gives 2x2 – xy – 3y2.

Choice A is incorrect and may be the result of using the sums of the coefficients of the existing x and y terms as the coefficients of the x and y terms in the new expressions. Choice C is incorrect and may be the result of incorrectly combining like terms. Choice D is incorrect and may be the result of using the incorrect sign in front of the 12y term.