{"id":"cb_question_bank:2df40af9-7dc5-4be7-b68e-8909b1b67c10","source_id":"cb_question_bank","source_item_id":"2df40af9-7dc5-4be7-b68e-8909b1b67c10","external_id":"5d93e88d-9666-4e29-baab-4dcd15423597","ibn":null,"question_id":"70482e20","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 expression is equivalent to 11 x cubed minus 5 x cubed ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to <math alttext=\"11 x cubed minus 5 x cubed\"><mrow><mn>11</mn></mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mrow><mn>5</mn></mrow><msup><mi>x</mi><mn>3</mn></msup></math>?</p>","rationale_html":"<p>Choice B is correct. The given expression can be rewritten as <math alttext=\"11 x cubed plus left parenthesis negative 5 right parenthesis x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><msup><mi>x</mi><mn>3</mn></msup></math>. Since the two terms of this expression are both constant multiples of <math alttext=\"x cubed\"><msup><mi>x</mi><mn>3</mn></msup></math>, they are like terms and can, therefore, be combined through addition. Adding like terms in the expression <math alttext=\"11 x cubed plus left parenthesis negative 5 right parenthesis x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfenced><msup><mi>x</mi><mn>3</mn></msup></math> yields <math alttext=\"6 x cubed\"><mn>6</mn><msup><mi>x</mi><mn>3</mn></msup></math>.</p>\n<p>Choice A is incorrect. This is equivalent to&nbsp;<math alttext=\"11 x cubed plus 5 x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></math>, not&nbsp;<math alttext=\"11 x cubed minus 5 x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></math>.</p>\n<p>Choice C is incorrect. This is equivalent to&nbsp;<math alttext=\"11 x Superscript 6 minus 5 x Superscript 6\"><mn>11</mn><msup><mi>x</mi><mn>6</mn></msup><mo>-</mo><mn>5</mn><msup><mi>x</mi><mn>6</mn></msup></math>, not&nbsp;<math alttext=\"11 x cubed minus 5 x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></math>.&nbsp;</p>\n<p>Choice D is incorrect. This is equivalent to&nbsp;<math alttext=\"11 x Superscript 6 plus 5 x Superscript 6\"><mn>11</mn><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>5</mn><msup><mi>x</mi><mn>6</mn></msup></math>, not&nbsp;<math alttext=\"11 x cubed minus 5 x cubed\"><mn>11</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup></math>.&nbsp;</p>","correct_answer":["B"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.822000+00:00","source_updated_at":"2023-08-02T20:25:59.822000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"16 x cubed\"><mrow>\n\t<mn>16</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>3</mn>\n\t</msup>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"6 x cubed\"><mrow>\n\t<mn>6</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>3</mn>\n\t</msup>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"6 x Superscript 6\"><mrow>\n\t<mn>6</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>6</mn>\n\t</msup>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"16 x Superscript 6\"><mrow>\n\t<mn>16</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>6</mn>\n\t</msup>\n</mrow>\n</math></p>","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}}