{"id":"cb_question_bank:bf251f6b-7de1-4dc7-a141-15f0e5196708","source_id":"cb_question_bank","source_item_id":"bf251f6b-7de1-4dc7-a141-15f0e5196708","external_id":null,"ibn":"029468-DC","question_id":"c3a72da5","program":"SAT","module":"math","domain_code":"P","domain":"Advanced Math","skill_code":"P.A.","skill":"Equivalent expressions","difficulty":"M","score_band":4,"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 the sum of 3 x to the fourth power, plus 2 x cubed and 4 x to the fourth power, plus 7 x cubed ?","stimulus":"","stimulus_html":null,"stem_html":"<p class=\"stem_paragraph \">Which of the following is equivalent to the sum of <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ad30160a5dd752cbe89d39fac6ef7914b78df035d2957630492c5148ad7edab0\" alt=\"3 x to the fourth power, plus 2 x cubed\"></span></span> and <span class=\"math_expression \"><span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/8e39bd0b6d22be09bd704031ee1e853832c9a5cf9a8d8d196cb1778f0c673801\" alt=\"4 x to the fourth power, plus 7 x cubed\"></span></span>?</p>\n","rationale_html":"<p>Choice D is correct. Adding the two expressions yields <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d7ae85e02d462e669bf43e6df161115957e2cdea173d35ea784a66fd17599bd6\" alt=\"3 x to the fourth power, plus 2 x to the third power, plus 4 x to the fourth power, plus 7 x to the third power\"></span>. Because the pair of terms <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/534c27475abe68f87941e3137f12964116527dd0a5b0575fb46fafe20ffcac9e\" alt=\"3 x to the fourth power \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/7ac751e2c8847591cb2b98f139d2161b0329456c0f520605f0a9227a84cb9bbb\" alt=\"4 x to the fourth power\"></span> and the pair of terms <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/d5615ad095c0778a18886c6d4025d5230f339a26f252ae601b757cea0db2f6f2\" alt=\"2 x to the third power \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/35caf654218b9fa9a987aeb4d3f0c05eb77efa0207b1e62e9aaeb4fe52602c88\" alt=\"7 x to the third power \"></span> each contain the same variable raised to the same power, they are like terms and can be combined as <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/ee067d7170777f46c5babd227271d087a8a23aa72e1a1ad537b66ac57483840f\" alt=\"7 x to the fourth power \"></span> and <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/e04e7f224511d2946238c96766ccefcf6facca99ef7c17d149d4efa41a5a34ed\" alt=\"9 x to the third power\"></span>, respectively. The sum of the given expressions therefore simplifies to <span class=\"math-container\"><img align=\"middle\" role=\"math\" class=\"math-img\" src=\"/api/assets/dbb9dfbec121b99d0a5abeb113532911fd3e433023bce217183137a69d83090a\" alt=\"7 x to the fourth power, plus 9 x to the third power\"></span>.</p><p>Choice A is incorrect and may result from adding the coefficients and the exponents in the given expressions. Choice B is incorrect and may result from adding the exponents as well as the coefficients of the like terms in the given expressions. Choice C is incorrect and may result from multiplying, rather than adding, the coefficients of the like terms in the given expressions.</p><p></p>\n","correct_answer":["D"],"has_media":true,"has_mathml":false,"has_table":false,"source_created_at":"2023-08-02T20:25:59.625000+00:00","source_updated_at":"2023-08-02T20:25:59.625000+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/d371d0e2df80c52c97fb4a20c88b9d98c95ab84c5d2ddaf1a617b544e06936bf\" alt=\"16 x to the fourteenth power\"></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/aaeda007810ffece22acfb7a3f0ebcac56a01b72b6e2dd43161acb1c2679d709\" alt=\"7 x to the eighth power, plus 9 x to the sixth power\"></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/9726ef5d45645c2e9d24d68d4a4214d245cf2bb616630c8c1e999eff177b7e7d\" alt=\"12 x to the fourth power, plus 14 x cubed\"></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/dbb9dfbec121b99d0a5abeb113532911fd3e433023bce217183137a69d83090a\" alt=\"7 x to the fourth power, plus 9 x cubed\"></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}}