(3) Which expression is equivalent to $$ 3(2 x+4 y)-y $$ ? A $$ 17 x y $$ B $$ 6 x+12 $$ C $$ 3(6 x y)-y $$ D $$ 6(x+2 y)-y $$ Kimani chose C as the correct answer. How might she have gotten that answer?

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UpStudy AI · Accepted Answer

1. Kimani started with the expression  
   $$
   3(2x+4y)-y.
   $$

2. She mistakenly “combined” the terms $$2x$$ and $$4y$$ as if they were like terms. In her reasoning, she treated the sum as:  
   $$
   2x+4y \stackrel{\text{incorrectly}}{=} (2+4)xy = 6xy.
   $$

3. Then, substituting her incorrect combination into the original expression, she obtained:  
   $$
   3(2x+4y)-y = 3(6xy)-y.
   $$

4. This is exactly answer C, although the error lies in assuming that $$2x$$ and $$4y$$ could be added by combining their numerical coefficients and then multiplying by $$xy$$.

In reality, because $$x$$ and $$y$$ are different variables, the terms $$2x$$ and $$4y$$ are not like terms and cannot be combined in that way. The proper approach would have been to distribute:  
$$
3(2x+4y)-y = 6x + 12y - y = 6x + 11y.
$$
Kimani likely combined the terms $$2x$$ and $$4y$$ incorrectly by adding their coefficients, thinking $$2x + 4y = 6xy$$, and then multiplied by 3 to get $$3(6xy) - y$$, which matches option C.

(3) Which expression is equivalent to \( 3(2 x+4 y)-y \) ? A \( 17 x y \) B \( 6 x+12 \) C \( 3(6 x y)-y \) D \( 6(x+2 y)-y \) Kimani chose C as the correct answer. How might she have gotten that answer?

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