{"id":"cb_question_bank:a3fb785e-b43a-4fec-b32a-4d66979afb50","source_id":"cb_question_bank","source_item_id":"a3fb785e-b43a-4fec-b32a-4d66979afb50","external_id":null,"ibn":"00094-DC","question_id":"ad038c19","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":6,"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 parenthesis, a, plus the fraction b over 2, close parenthesis, squared ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d5bc55cead7e9c25ccfc568d44b7d726b93394f2a2a1de08b48f9f420f8158f\" alt=\"parenthesis, a, plus the fraction b over 2, close parenthesis, squared\"></span></span> ?</p>\n","rationale_html":"<p>Choice D is correct. The expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/5d5bc55cead7e9c25ccfc568d44b7d726b93394f2a2a1de08b48f9f420f8158f\" alt=\"open parenthesis, a, plus the fraction b over 2, close parenthesis, squared\"></span> can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/f49b03b54c4a4e338ebaec0478e17ee5e93a679ce51d68003266dfba90c58f4f\" alt=\"open parenthesis, a, plus the fraction b over 2, close parenthesis, times, open parenthesis, a, plus the fraction b over 2, close parenthesis\"></span>. Using the distributive property, the expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ba07c283f70ee85e80d842d848ce909a2ab83b7b47bd4e3e844d8de6987e0fc5\" alt=\"open parenthesis, a, plus the fraction b over 2, close parenthesis, times, open parenthesis, a, plus the fraction b over 2, close parenthesis, equals, a, squared, plus the fraction with numerator a, b and denominator 2, end fraction, plus the fraction with numerator a, b and denominator 2, end fraction, plus the fraction b squared, over 4\"></span>. Combining like terms gives <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1c7b2da865766a08d6661cabaf8ec4b6a90226a0464cb02d19acc1e4885f469c\" alt=\"a, squared, plus a, b, plus the fraction b squared over 4\"></span>.</p><p>Choices A, B, and C are incorrect and may result from errors using the distributive property on the given expression or combining like terms.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.613000+00:00","source_updated_at":"2023-08-02T20:25:59.613000+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/c6eb27aae961d712bbf96a558fa7fdd17e30ae0675dbbb14d25d022df49db99b\" alt=\"a, squared, plus the fraction b squared over 2\"></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/e7538cdfa08c2d2c1dcfcf3e8c1fc1c86f9608f3280ae3d8f2172070243151e1\" alt=\"a, squared, plus the fraction b squared over 4\"></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/cb89f7670d9bd50b708ff5ade16928d90dec6bb6e8ca3c47ed8585123ca57457\" alt=\"a, squared, plus the fraction a, times b, over 2, end fraction, plus the fraction b squared over 2\"></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/1c7b2da865766a08d6661cabaf8ec4b6a90226a0464cb02d19acc1e4885f469c\" alt=\"a, squared, plus a, times b, plus the fraction b squared over 4\"></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}}