{"id":"cb_question_bank:fe8889cf-eeea-4460-83f0-4adf594c98f1","source_id":"cb_question_bank","source_item_id":"fe8889cf-eeea-4460-83f0-4adf594c98f1","external_id":null,"ibn":"017096-DC","question_id":"974d33dc","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 expressions is equivalent to the sum of open parenthesis, r cubed, plus 5 r squared, plus 7, close parenthesis and open parenthesis, r squared, plus 8 r, plus 12, close parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following expressions is equivalent to the sum of <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d43e760572e964874d3ebfcf406d3e9f5c3b13e881079d4911015573c0ad953\" alt=\"open parenthesis, r cubed, plus 5 r squared, plus 7, close parenthesis\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/50deb01e5f2edd605300b571d2dd359fa2745f6a32ea135757a478787183a784\" alt=\"open parenthesis, r squared, plus 8 r, plus 12, close parenthesis\"></span> ?</p>\n","rationale_html":"<p>Choice D is correct. Grouping like terms, the given expressions can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/57ff4f54d42154a2a061279514c3e443d54601da694f92efc24e20d7150463de\" alt=\"r cubed plus, open parenthesis, 5, r squared plus r squared, close parenthesis, plus 8 r, plus, open parenthesis, 7 plus 12, close parenthesis\"></span>. This can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a58a5c428077de3cfcbe92db50b85b7414a79291e0dd01c02e1335dd253ff1e7\" alt=\"r cubed, plus 6, r squared, plus 8 r, plus 19\"></span>.</p><p>Choice A is incorrect and may result from adding the two sets of unlike terms, <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7f91670bc0ffc308c2d114ad18ab71b74ede894ba0ef2c8539193cfb39053b2\" alt=\"r cubed\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eb51eb71b005a4126a38b65411746fe3fa6367ce83392513168f067368c29e01\" alt=\"r squared\"></span> as well as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6cbd3c5a387f5b3fa8851d44213494a5365500db040c0c089eef273764c6567b\" alt=\"5, r squared \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e62b9d82e10eebf1620c37f072889c313d12efbea83fc6927c644af409ae3a22\" alt=\"8 r\"></span>, and then adding the respective exponents. Choice B is incorrect and may result from adding the unlike terms&nbsp;<span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7f91670bc0ffc308c2d114ad18ab71b74ede894ba0ef2c8539193cfb39053b2\" alt=\"r cubed\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/eb51eb71b005a4126a38b65411746fe3fa6367ce83392513168f067368c29e01\" alt=\"r squared\"></span> as if they were <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7f91670bc0ffc308c2d114ad18ab71b74ede894ba0ef2c8539193cfb39053b2\" alt=\"r cubed\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e7f91670bc0ffc308c2d114ad18ab71b74ede894ba0ef2c8539193cfb39053b2\" alt=\"r cubed\"></span> and adding the unlike terms <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6cbd3c5a387f5b3fa8851d44213494a5365500db040c0c089eef273764c6567b\" alt=\"5, r squared\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e62b9d82e10eebf1620c37f072889c313d12efbea83fc6927c644af409ae3a22\" alt=\"8 r\"></span> as if they were <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6cbd3c5a387f5b3fa8851d44213494a5365500db040c0c089eef273764c6567b\" alt=\"5, r squared\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ae712a5624947c910922f85854987a7ab36d3235dae82e217bc49c6b92b7821b\" alt=\"8, r squared\"></span>. Choice C is incorrect and may result from errors when combining like terms.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.615000+00:00","source_updated_at":"2023-08-02T20:25:59.615000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1fb9215a3a5214735c2cb5bc38f9e89d932cf30606221b300a87044ae5ed234b\" alt=\"r to the fifth power, plus 13 r cubed, plus 19\"></span></span></p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/edf13192b973a43a05c63700d057a96387c88b35e6e579eb7899fcbf1afb5266\" alt=\"2 r cubed, plus 13 r squared, plus 19\"></span></span></p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f1707cd59db6ab3abb15cca5443857d9665ecada7a940f0cbabd99eedc4d4848\" alt=\"r cubed, plus 5 r squared, plus 7 r, plus 12\"></span></span></p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \"><span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a58a5c428077de3cfcbe92db50b85b7414a79291e0dd01c02e1335dd253ff1e7\" alt=\"r cubed, plus 6 r squared, plus 8 r, plus 19\"></span></span></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}}