{"id":"cb_question_bank:87896da4-48cf-40fc-8cae-8aca2dc48153","source_id":"cb_question_bank","source_item_id":"87896da4-48cf-40fc-8cae-8aca2dc48153","external_id":"322bacf8-a04d-4c31-8a29-228d7b8ccca3","ibn":null,"question_id":"26eb61c1","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":"Which expression is equivalent to 6 x Superscript 8 Baseline y squared plus 12 x squared y squared ?","stimulus":"","stimulus_html":null,"stem_html":"<p>Which expression is equivalent to <math alttext=\"6 x Superscript 8 Baseline y squared plus 12 x squared y squared\"><mrow>\n\t<mrow>\n\t\t<mn>6</mn>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>8</mn>\n\t\t</msup>\n\t\t<msup>\n\t\t\t<mi>y</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>12</mn>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t\t<msup>\n\t\t\t<mi>y</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t</mrow>\n</mrow>\n</math>?</p>","rationale_html":"<p>Choice C is correct. Since each term of the given expression has a common factor of <math alttext=\"6 x squared y squared\"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>, it may be rewritten as <math alttext=\"6 x squared y squared left parenthesis x Superscript 6 Baseline right parenthesis plus 6 x squared y squared left parenthesis 2 right parenthesis\"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>(</mo><msup><mi>x</mi><mn>6</mn></msup><mo>)</mo><mo>+</mo><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>(</mo><mn>2</mn><mo>)</mo></math>, or <math alttext=\"6 x squared y squared left parenthesis x Superscript 6 Baseline plus 2 right parenthesis\"><mn>6</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>(</mo><msup><mi>x</mi><mn>6</mn></msup><mo>+</mo><mn>2</mn><mo>)</mo></math>.</p>\n<p>Choice A is incorrect. This expression is equivalent to <math alttext=\"12 x Superscript 8 Baseline y squared\"><mn>12</mn><msup><mi>x</mi><mn>8</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>, not <math alttext=\"6 x Superscript 8 Baseline y squared plus 12 x squared y squared\"><mn>6</mn><msup><mi>x</mi><mn>8</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>.</p>\n<p>Choice B is incorrect. This expression is equivalent to <math alttext=\"6 x Superscript 6 Baseline y squared\"><mn>6</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>, not <math alttext=\"6 x Superscript 8 Baseline y squared plus 12 x squared y squared\"><mn>6</mn><msup><mi>x</mi><mn>8</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>.</p>\n<p>Choice D is incorrect. This expression is equivalent to <math alttext=\"6 x Superscript 6 Baseline y squared plus 12 x squared y squared\"><mn>6</mn><msup><mi>x</mi><mn>6</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>, not <math alttext=\"6 x Superscript 8 Baseline y squared plus 12 x squared y squared\"><mn>6</mn><msup><mi>x</mi><mn>8</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup></math>.</p>","correct_answer":["C"],"has_media":false,"has_mathml":true,"has_table":false,"source_created_at":"2023-08-02T20:25:59.821000+00:00","source_updated_at":"2023-08-02T20:25:59.821000+00:00","options":[{"label":"A","content_html":"<p><math alttext=\"6 x squared y squared left parenthesis 2 x Superscript 6 Baseline right parenthesis\"><mrow><mn>6</mn></mrow><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mfenced><mrow><mrow><mn>2</mn></mrow><msup><mi>x</mi><mrow><mn>6</mn></mrow></msup></mrow></mfenced></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"6 x squared y squared left parenthesis x Superscript 4 Baseline right parenthesis\"><mrow><mn>6</mn></mrow><msup><mi>x</mi><mn>2</mn></msup><msup><mi>y</mi><mn>2</mn></msup><mfenced><msup><mi>x</mi><mrow><mn>4</mn></mrow></msup></mfenced></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"6 x squared y squared left parenthesis x Superscript 6 Baseline plus 2 right parenthesis\"><mrow>\n\t<mn>6</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>2</mn>\n\t</msup>\n\t<msup>\n\t\t<mi>y</mi>\n\t\t<mn>2</mn>\n\t</msup>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<msup>\n\t\t\t\t<mi>x</mi>\n\t\t\t\t<mn>6</mn>\n\t\t\t</msup>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>2</mn>\n\t\t</mrow>\n\t</mfenced>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"6 x squared y squared left parenthesis x Superscript 4 Baseline plus 2 right parenthesis\"><mrow>\n\t<mn>6</mn>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>2</mn>\n\t</msup>\n\t<msup>\n\t\t<mi>y</mi>\n\t\t<mn>2</mn>\n\t</msup>\n\t<mfenced>\n\t\t<mrow>\n\t\t\t<msup>\n\t\t\t\t<mi>x</mi>\n\t\t\t\t<mn>4</mn>\n\t\t\t</msup>\n\t\t\t<mo>+</mo>\n\t\t\t<mn>2</mn>\n\t\t</mrow>\n\t</mfenced>\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}}