{"id":"cb_question_bank:c7e0ffcd-cb85-4ea3-be4d-6dc522beeba4","source_id":"cb_question_bank","source_item_id":"c7e0ffcd-cb85-4ea3-be4d-6dc522beeba4","external_id":null,"ibn":"025717-DC","question_id":"df0ef054","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":3,"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, 2 x cubed, plus 3 x, close parenthesis, times, open parenthesis, x cubed, minus 2 x, 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/fc65f774e6d0ca5158447369523531c1e0326dfe06793ecec5debeeda071c8bc\" alt=\"open parenthesis, 2 x cubed, plus 3 x, close parenthesis, times, open parenthesis, x cubed, minus 2 x, 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 C is correct. Using the distributive property to multiply the terms in the parentheses yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6281b22fd8f2852ca46c24523b8060325e9a17d7f4f26074d65813cebed90332\" alt=\"open parenthesis, 2 x cubed, times x cubed, close parenthesis, plus, open parenthesis, 2 x cubed, times negative 2 x, close parenthesis, plus, open parenthesis, 3 x times x cubed, close parenthesis, plus, open parenthesis, 3 x times negative 2 x, close parenthesis\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c94e4827e75dd2665cf6c6d2a14cca3fffbe976455c94e36a9f1690490ac1a07\" alt=\"2 x to the sixth power minus 4 x to the fourth power, plus 3 x to the fourth power, minus 6 x squared\"></span>. Combining like terms results in&nbsp; <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/be07793c56dcb65fe0b962e26f2729bbef6906be723bafd8c4389d731420315a\" alt=\"2 x to the sixth power minus x to the fourth power, minus 6 x squared\"></span>.</p><p>Choices A and D are incorrect and may result from conceptual errors when multiplying the terms in the given expression. Choice B is incorrect and may result from adding, instead of multiplying, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b9a012e376ce116503c17e21349c30ae4634ccaf5e2038c7c986de8647be4244\" alt=\"open parenthesis, 2 x cubed, plus 3 x, close parenthesis \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f63ba157a4f493ca78e03c7eac7c66683f0a0a52f1568ee16f1bbf8f84b911fe\" alt=\"open parenthesis, x cubed, minus 2 x, close parenthesis\"></span>.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.619000+00:00","source_updated_at":"2023-08-02T20:25:59.619000+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/59494793b60d6d9ec3f6bdf01609f62f54139088908d89d55e0c7113b6ba4d5a\" alt=\"x cubed, plus 5 x\"></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/78ea4ddf841bcc6a7d5a286331496ea848c683e4e9bea89c030f9e4ba7f54a3d\" alt=\"3 x cubed, plus x\"></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/be07793c56dcb65fe0b962e26f2729bbef6906be723bafd8c4389d731420315a\" alt=\"2 x to the sixth power, minus x to the fourth power, minus 6 x 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/145679515a123ce96c3bae751472459d926961122d4bdf730dfe51568dd14bde\" alt=\"3 x to the sixth power, minus x to the fourth power, minus 6 x 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}}