Here's an example
<span>Simplify by collecting like terms: 4(<span>x2y </span>+ 7y) – 5y(3<span>x2 </span>– y) – 10y</span>
<span>A) −11x2y + 5<span>y2 </span>+ 18y</span>
<span>B) 4<span>x2y + </span>11y – 8<span>yx2 – </span>16y</span>
<span>C) 4<span>x2y + </span>18y – 15<span>yx2 + </span>5<span>y2</span></span>
<span>D) 4<span>x2y </span>– 5y(3<span>x2 </span>– y) – 3y</span>
<span>A) −11x2y + 5<span>y2 </span>+ 18y </span>
<span>Correct. 4(<span>x2y </span>+ 7y) – 5<span>y(3x2 </span>– y) – 10y = 4<span>x2y + </span>28y – 15<span>yx2</span> + 5<span>y2 – </span>10y = 4<span>x2y + </span>18y – 15<span>yx2</span> + 5<span>y2 </span>= −11x2y + 5<span>y2 </span>+ 18y.</span>
<span>B) 4<span>x2y + </span>11y – 8<span>yx2 – </span>16y </span>
<span>Incorrect. The 4 is distributed to both terms in the parentheses by multiplying each term by 4 resulting in 28y, not 11y. The −5y is similarly distributed to each term in the parentheses, resulting in −15<span>yx2 + </span>5<span>y2. </span>The correct answer is −11x2y + 5<span>y2 </span>+ 18y.</span>
<span>C) 4<span>x2y + </span>18y – 15<span>yx2 + </span>5<span>y2</span></span>
<span>Incorrect. This polynomial can be further simplified by combining the like terms 4<span>x2y </span>and −15<span>yx2. </span>The order of the variables in a term does not matter. The correct answer is </span>
−<span>11x2y + 5<span>y2 </span>+ 18y.</span>
<span>D) 4<span>x2y </span>– 5y(3<span>x2 </span>– y) – 3y </span>
<span>Incorrect. Before combining like terms, you must distribute to clear the parentheses. The correct answer is −11x2y + 5<span>y2 </span>+ 18y.</span>
. This is proved by the fact that the distance between each corner ABC to the mirror line equals to the distance between the mirror line to A'B'C'.
