{"id":"act_quizme:math:q3:03","source_id":"act_quizme","source_item_id":"math-q3-03","external_id":"88aff840e1bfcaf3","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":3,"scored":true,"layout_warning":null,"stem":"Which of the following expressions is equivalent to (x squared minus y squared) minus (6x squared +4xy minus y squared) ( x 2 - y 2 ) - ( 6 x 2 + 4 x y - y 2 ) ?","stimulus":"","stimulus_html":null,"stem_html":"
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Which of the following expressions is equivalent to (x squared minus y squared) minus (6x squared +4xy minus y squared)(x2-y2)-(6x2+4xy-y2)?

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","rationale_html":"

A. Correct. First, apply the distributive property: x2-y2-6x2+4xy-y2=x2-y2-6x2-4xy+y2. Next, group like terms to get x2-6x2-4xy-y2+y2. Finally, combine like terms to get -5x2-4xy.

B. Incorrect. When applying the distributive property, be sure that the negative gets distributed to all terms of the trinomial: x2-y2-6x2+4xy-y2=x2-y2-6x2-4xy+y2. You may not have multiplied the last 2 terms by -1.

C. Incorrect. Be sure to apply the distributive property to distribute the negative through the trinomial: x2-y2-6x2+4xy-y2=x2-y2-6x2-4xy+y2. You may have ignored the negative sign and thus calculated x2-y2+6x2+4xy-y2 or 7x2+4xy-2y2.

D. Incorrect. Be careful with the signs when applying the distributive property. You may have used a plus sign wherever there was a minus sign to get x2+y2+6x2+4xy+y2 or 7x2+4xy+2y2.

","correct_answer":["A"],"equiv_key":"578aa94972a1c7c55766f134","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"

negative 5x squared minus 4xy-5x2-4xy

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negative 5x squared +4xy minus 2y squared-5x2+4xy-2y2

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7x squared +4xy minus 2y squared7x2+4xy-2y2

","ord":2},{"label":"D","content_html":"

7x squared +4xy+2y squared7x2+4xy+2y2

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