{"id":"cb_question_bank:f5195c2f-b319-4461-9bb3-49a77d44ea36","source_id":"cb_question_bank","source_item_id":"f5195c2f-b319-4461-9bb3-49a77d44ea36","external_id":null,"ibn":"05799-DC","question_id":"c602140f","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is equivalent to the expression above?","stimulus":"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","stimulus_html":"<div class=\"stimulus_reference \">\n        <p class=\"standalone_statement style:1 \">\n          <span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e780c6af180241cd14f0ad932cde2ffe702872ae1deed3669c22b7c85cb6edaf\" alt=\"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\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to the expression above?</p>\n","rationale_html":"<p>Choice B is correct. Expanding&nbsp;all terms yields&nbsp;(<span class=\"italic\">x</span> – 11<span class=\"italic\">y</span>)(2<span class=\"italic\">x</span> – 3<span class=\"italic\">y</span>) – 12<span class=\"italic\">y</span>(–2<span class=\"italic\">x</span> + 3<span class=\"italic\">y</span>), which is equivalent to&nbsp;2<span class=\"italic\">x</span><sup>2</sup> – 22<span class=\"italic\">xy</span> – 3<span class=\"italic\">xy</span> + 33<span class=\"italic\">y</span><sup>2</sup> + 24<span class=\"italic\">xy</span> – 36<span class=\"italic\">y</span><sup>2</sup>. Combining like terms gives 2<span class=\"italic\">x</span><sup>2</sup> – <span class=\"italic\">xy</span> – 3<span class=\"italic\">y</span><sup>2</sup>.</p><p>Choice A is incorrect and may be the result of using the sums of the coefficients of the existing <span class=\"italic\">x</span> and <span class=\"italic\">y</span> terms as the coefficients of the <span class=\"italic\">x</span> and <span class=\"italic\">y</span> terms in the new expressions.&nbsp;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 12<span class=\"italic\">y</span> term.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.630000+00:00","source_updated_at":"2023-08-02T20:25:59.630000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/71bfeee3a728beb4f020b8b63bca1c750e795114bbd3a8a6f80935182619f4f8\" alt=\"x minus 23 y\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/9842ff3eac1395c133949c9fc9a5afa4bd284f4d631827d01c7d50cdfc7a7108\" alt=\"2 x squared, minus x y, minus 3 y squared\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/11eb5eec8ba8761ed8de1d03793ecb33e059de433a876983daac565796eabc9b\" alt=\"2 x squared, plus 24 x y, plus 36 y squared\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f900c29293bcd2f44cb7da14c19824d2b26d34ba815ca68200a21d13e91519dd\" alt=\"2 x squared, minus 49 x y, plus 69 y squared\"></span></span>\n          </p>\n","ord":3}],"attribution":{"source_id":"cb_question_bank","source_name":"College Board digital SAT question bank (community dump)","rights_holder":"College Board","canonical_url":"https://satsuitequestionbank.collegeboard.org/","retrieved_from":"https://raw.githubusercontent.com/mdn522/sat-question-bank/main/data/cb-digital-questions.json","attribution":"SAT practice questions © College Board, from the official SAT Suite Question Bank. Retrieved via the community dump at github.com/mdn522/sat-question-bank.","disclaimer":"SAT® and PSAT/NMSQT® are trademarks registered by the College Board, which is not affiliated with, does not sponsor, and does not endorse this project.","license":"College Board copyright; source repository carries no licence. Local use only.","redistributable":false,"item_count":2017}}