{"id":"cb_question_bank:2520d50d-5fdf-4439-a9ad-ed8c8acd9a88","source_id":"cb_question_bank","source_item_id":"2520d50d-5fdf-4439-a9ad-ed8c8acd9a88","external_id":null,"ibn":"05410-DC","question_id":"cc776a04","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":5,"answer_type":"mcq","answer_source":"key","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"Which of the following is an equivalent form of open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, squared, minus, open parenthesis, 5 point 2, x squared, minus 6 point 4, close parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is an equivalent form of <span class=\"math_expression \"></span><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/b93ed3884fd4a30498194e7fba5503e13df023526dfd58592776345893a5a007\" alt=\"open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, squared, minus, open parenthesis, 5 point 2, x squared, minus 6 point 4, close parenthesis\"></span> ?</p>\n","rationale_html":"<p>Choice C is correct. The first expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/18b35f4b35d0513c305280f0eb3d43bc1b0984efce7768120f6ae08998e6332d\" alt=\"open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, squared\"></span> can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/424c56e2a9a5275cb34ce74782ce3e736148f0b67fa1d4c1be4a5d556a8d29ab\" alt=\"open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis, times, open parenthesis, 1 point 5 x minus 2 point 4, close parenthesis\"></span> . Applying the distributive property to this product yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c41022f7a97a581fe7a1c6b600f82c75e44ddeb5eb643d0c7a8715cb72ad2b7f\" alt=\"open parenthesis, 2 point 2 5, x squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, close parenthesis, minus, open parenthesis, 5 point 2, x squared, minus 6 point 4, close parenthesis\"></span> . This difference can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/687106341a4b0efa825ddb6e8e331e66d558f493cdc96dd5562024bd62d2812e\" alt=\"open parenthesis, 2 point 2 5, x squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, close parenthesis, plus, negative 1 times, open parenthesis, 5 point 2 x squared, minus 6 point 4, close parenthesis\"></span> . Distributing the factor of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c1e573ec087416273e06563cee97890abeeed317436562b06a92c8920d4c759d\" alt=\"negative 1\"></span> through the second expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/db810be1b1996331415bdfd71e45f45e071fa9646013d975d45599097818695d\" alt=\"2 point 2 5 x, squared, minus 3 point 6 x, minus 3 point 6 x, plus 5 point 7 6, minus 5 point 2, x squared, plus 6 point 4\"></span> . Regrouping like terms, the expression becomes <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/59636a0b7cf6e02fea307f68599b58d1065148c396d87a5ff0f950d2d90b0758\" alt=\"open parenthesis, 2 point 2 5, x squared, minus 5 point 2, x squared, close parenthesis, plus, open parenthesis, negative 3 point 6 x minus 3 point 6 x, close parenthesis, plus, open parenthesis, 5 point 7 6 plus 6 point 4, close parenthesis\"></span> . Combining like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f8ad02e27d993a4725207a29c517a13b9c120d63ed2bdb846cc4178e9a264be6\" alt=\"negative 2 point 9 5, x squared, minus 7 point 2 x, plus 12 point 1 6\"></span> .</p><p>Choices A, B, and D are incorrect and likely result from errors made when applying the distributive property or combining the resulting like terms.</p><p></p>\n","correct_answer":["C"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.629000+00:00","source_updated_at":"2023-08-02T20:25:59.629000+00:00","options":[{"label":"A","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/fc819bae0449656a15373d8e12a8052b2036ca7eb6561acc2b968e06cc554312\" alt=\"negative 2 point 2, x squared, plus 1 point 6\"></span></span>\n","ord":0},{"label":"B","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6bc0736322ab90d0d6e89199ca219f4dbd67d271df92f20dcafc59be8bbcbbd3\" alt=\"negative 2 point 2, x squared, plus 11 point 2\"></span></span>\n","ord":1},{"label":"C","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/47968609d96c0a7aa925e535604a196d21d1c24fc9d7213149fd20632eba9202\" alt=\"negative 2 point 95, x squared, minus 7 point 2 x, plus 12 point 16\"></span></span>\n","ord":2},{"label":"D","content_html":"<span class=\"math_expression \">\n            <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4d06163b1cb0f4b21dc4de6cc2258eacada3c904d3629de2eb821eb5f50a920c\" alt=\"negative 2 point 95, x squared, minus 7 point 2 x, plus 0 point 64\"></span></span>\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}}