{"id":"cb_question_bank:bfb0c12f-0536-4377-bf47-7816a0c39071","source_id":"cb_question_bank","source_item_id":"bfb0c12f-0536-4377-bf47-7816a0c39071","external_id":null,"ibn":"08605-DC","question_id":"911c415b","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"H","score_band":7,"answer_type":"spr","answer_source":"rationale","layout_warning":null,"form_id":null,"module_number":null,"position":null,"stem":"The expression above can be written in the form a, times y squared, plus b , where a and b are constants. What is the value of a, plus b ?","stimulus":"open parenthesis, 7,532, plus 100 y squared, close parenthesis, plus, 10 times open parenthesis, 10 y squared minus 110, 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/759c5a233732ac2fc9b576c8f70adb9015d3e9f13923dd62c8232cb2b0da05d8\" alt=\"open parenthesis, 7,532, plus 100 y squared, close parenthesis, plus, 10 times open parenthesis, 10 y squared minus 110, close parenthesis\"></span></span>\n        </p>\n      </div>\n","stem_html":"<p class=\"stem_paragraph \">The expression above can be written in the form <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee8e129c85734a83b4a3b0cbe39b78513558233cc43b24eba81978aa38a414ca\" alt=\"a, times y squared, plus b\"></span></span>, where <span class=\"italic\">a</span> and <span class=\"italic\">b</span> are constants. What is the value of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/90874e3b35f41c70a9a76eeaad2ae42db3d2ec2cd0593c162905d714304e8b8d\" alt=\"a, plus b\"></span></span> ?</p>\n","rationale_html":"<p>The correct answer is 6632. Applying the distributive property to the expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d51535079d15c2b1b526a47a2624aea82da79ba96d2dfbde692f4d5457c919b0\" alt=\"open parenthesis, 7532 plus 100 y squared, close parenthesis, plus, open parenthesis, 100 y squared, minus 1100, close parenthesis\"></span>. Then adding together <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/4d6da8e880338b07b29c89e221c71bcbfbc4a5a3bc35ee5473f8c237db944f61\" alt=\"7532 plus 100 y squared\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dff326853bb6d4adf37bba12347614c7746b3f437114262c959f8f1a8ff8f080\" alt=\"100 y squared, minus 1100\"></span> and collecting like terms results in <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/94462d0ebd544554347df48249cb36ef6f6e28cd2e2814f36aee782c7f26c553\" alt=\"200 y squared, plus 6432\"></span>. This is written in the form <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/6d0927c34fcbef1ff69cfe3297c665b60d68efc965dd4d9570c5581e99b865c3\" alt=\"a, y squared, plus b\"></span>, where <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/1adfa0695e9bb0fef62060798bda30ea43148d3da5808ec0f0d3fafcf7fbf1e4\" alt=\"a, equals 200 \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/a8d690fc0caa305c84d5ae6e4ed6a40b96f07345dc0e9db07d6bd23bd0b1773e\" alt=\"b equals 6432\"></span>. Therefore <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c14ba7376df046cb4391b375db40d3b9529ad9ca15e3afc534bcca9cc072dba3\" alt=\"a, plus b equals, 200 plus 6432, which equals 6632\"></span>.</p>\n","correct_answer":["6632"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.636000+00:00","source_updated_at":"2023-08-02T20:25:59.636000+00:00","options":[],"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}}