{"id":"cb_question_bank:3b7745f4-1277-4f2f-9d6c-8dcd82c8d59d","source_id":"cb_question_bank","source_item_id":"3b7745f4-1277-4f2f-9d6c-8dcd82c8d59d","external_id":null,"ibn":"07749-DC","question_id":"a255ae72","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":"If x squared equals, a, plus b and y squared equals, a, plus c , which of the following is equal to open parenthesis, x squared, minus y squared, close parenthesis, squared ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">If <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e704b27e388358e5ef3647e0c630205ceda65edac40357d62bcc8a0abab67235\" alt=\"x squared equals, a, plus b \"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/90a15a3d8d18b97ba658bc06952aa1f59359c442e8095acd59f289b373781062\" alt=\"y squared equals, a, plus c\"></span></span>, which of the following is equal to <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/c14d36cb9643971a9b9b995a61adf50dfeda7535abc841c6a157f57cbb3909c4\" alt=\"open parenthesis, x squared, minus y squared, close parenthesis, squared \"></span></span> ?</p>\n","rationale_html":"<p>Choice B is correct. It’s given that <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e704b27e388358e5ef3647e0c630205ceda65edac40357d62bcc8a0abab67235\" alt=\"x squared equals, a, plus b\"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/90a15a3d8d18b97ba658bc06952aa1f59359c442e8095acd59f289b373781062\" alt=\"y squared equals, a, plus c\"></span>. Using the distributive property, the expression <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/64ff84d91025efda3d3592106fe20a96c310aaeab6462c93354e906c75240e02\" alt=\"open parenthesis, x squared, minus y squared, close parenthesis, squared \"></span> can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/0484e901917a221c13a9e093b443cb7642ffa6b5c134a1d4fded94dd40ed6f56\" alt=\"open parenthesis, x squared, close parenthesis, squared, minus 2 x squared, times y squared, plus, open parenthesis, y squared, close parenthesis, squared\"></span>. Substituting <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/90874e3b35f41c70a9a76eeaad2ae42db3d2ec2cd0593c162905d714304e8b8d\" alt=\"a, plus b \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/154fab496336ba4065b27485cd84bd149fe6a335fedc5b792d113c7244f2ee87\" alt=\"a, plus c \"></span> for <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3a186314172bc239fb025135d8722d39ee39bfefe4e212836956158aa0b9ff08\" alt=\"x squared \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/728c0e4d174d051dae68400947ed6a9b36af1a008ccd441e54e6e1038bfce0f3\" alt=\"y squared\"></span>, respectively, in this expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/3957e5c93e04286f08849b0547281afaeda0395fcf70091d5f89724cd8c9f534\" alt=\"open parenthesis, a, plus b, close parenthesis, squared, minus, 2 times, open parenthesis, open parenthesis, a, plus b, close parenthesis, times, open parenthesis, a, plus c, close parenthesis, close parenthesis, plus, open parenthesis, a, plus c, close parenthesis, squared\"></span>. Expanding this expression yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d1b40ccedc7441bbaed82334ba393f93804a49ac83477adeb20c9e1b3c2ea427\" alt=\"open parenthesis, a, squared, plus 2 a, b, plus b squared, close parenthesis, minus, open parenthesis, 2 a, squared, plus 2 b c, plus 2 a, c, plus 2 a, b, close parenthesis, plus, open parenthesis, a, squared, plus 2 a, c, plus c squared, close parenthesis\"></span>. Combining like terms, this expression can be rewritten as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/51628e24806fb5edadd664acead1333300b2400a087a76727731999aafb625f6\" alt=\"b squared, minus 2 b c, plus c squared\"></span>.</p><p>Choices A, C, and D are incorrect and may result from an error in using the distributive property, substituting, or combining like terms.</p><p></p>\n","correct_answer":["B"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.634000+00:00","source_updated_at":"2023-08-02T20:25:59.634000+00:00","options":[{"label":"A","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/54b5b0f452cf4b2ac1d3cb5d73afaebdf0852c1c673652783389189b92543792\" alt=\"a, squared, minus 2 a, c, plus c squared\"></span></span>\n          </p>\n","ord":0},{"label":"B","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/51628e24806fb5edadd664acead1333300b2400a087a76727731999aafb625f6\" alt=\"b squared, minus 2 b c, plus c squared\"></span></span>\n          </p>\n","ord":1},{"label":"C","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/40895ac161306898a78eb96590971bdd10543df25b8310dc35ce03d4345997e9\" alt=\"4, a, squared, minus 4 a, b c, plus c squared\"></span></span>\n          </p>\n","ord":2},{"label":"D","content_html":"<p class=\"choice_paragraph \">\n            <span class=\"math_expression \">\n              <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/50ecb3a019025ecde4bc9545a3cf82b8fbcf54e3ca1733b8d468311ea48b9d3a\" alt=\"4 a, squared, minus 2 a, b c, plus b squared c squared \"></span></span>\n          </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}}