{"id":"cb_question_bank:a348bae9-0d28-4172-89aa-0442df69792b","source_id":"cb_question_bank","source_item_id":"a348bae9-0d28-4172-89aa-0442df69792b","external_id":null,"ibn":"029332-DC","question_id":"6e06a0a7","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"E","score_band":2,"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 2, a squared, times, open parenthesis, a, plus 3, close parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following expressions is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/da87fac43f28a41f9141e9bc4bf247f9aa7d28f56bfbf4bd88a8ef86454fc49e\" alt=\"2, a squared, times, open parenthesis, a, plus 3, close parenthesis \"></span>&nbsp;?</span></p>\n","rationale_html":"<p>Choice D is correct. Expanding the given expression using the distributive property yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/bd6e5349098208b837dc012860028488e972fbce27874d98accaa6cf5b655c89\" alt=\"2 a, squared times, a, plus 2 a, squared times, 3\"></span>. Combining like terms yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f92eefd2ef1f8168f449ed0602349530582cdbbc95ea199e353a75dfb1bd3d68\" alt=\"2 a, squared times, open parenthesis, a, to the first power, close parenthesis, plus, open parenthesis, 2 times 3, close parenthesis, times, open parenthesis, a, squared, close parenthesis\"></span>, or <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ed53b744172d24954dc3f8de1081e46ad89310586233c0f99537fd7459c47854\" alt=\"2 a, raised to the 2 plus 1 power, plus 6 a, squared\"></span>, which is equivalent to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/835589d9d1dcdc362dd24a03465cca873b9901168d844f448ba96c7c208738f4\" alt=\"2 a, cubed, plus 6 a, squared\"></span>.</p><p>Choices A and B are incorrect and may result from incorrectly combining like terms. Choice C is incorrect and may result from distributing <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c8517a02443088bd476b364e2c84a34c6d3fc124f230b1eaadf8c54ad68d02c8\" alt=\"2 a, squared \"></span> only to <span class=\"italic\">a</span>, and not to 3, in the given expression.</p><p>&nbsp;</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.624000+00:00","source_updated_at":"2023-08-02T20:25:59.624000+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/903a96a9a66c4e41df3f9bb93be5f52f825cb2f47e86c15ae294aabb2395f58b\" alt=\"5, a cubed\"></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/00b6b52d4c984aec6f8810a97a016e52e649020aae46843a2b0409a5152aa458\" alt=\"8, a to the fifth power\"></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/a77fadefed6cc81f1b09c53306b8dcc42735706a9db248c7d8ec7440a919f060\" alt=\"2, a cubed, plus 3\"></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/835589d9d1dcdc362dd24a03465cca873b9901168d844f448ba96c7c208738f4\" alt=\"2, a cubed, plus 6, a squared\"></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}}