{"id":"cb_question_bank:7befdc0b-178a-44d3-87a0-bb4fac363e4e","source_id":"cb_question_bank","source_item_id":"7befdc0b-178a-44d3-87a0-bb4fac363e4e","external_id":"891c7c48-227c-4992-acdb-e5e19b360217","ibn":null,"question_id":"5805e747","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 expression is equivalent to left parenthesis 7 x cubed plus 7 x right parenthesis minus left parenthesis 6 x cubed minus 3 x right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression is equivalent to <math alttext=\"left parenthesis 7 x cubed plus 7 x right parenthesis minus left parenthesis 6 x cubed minus 3 x right parenthesis\"><mfenced><mrow><mrow><mn>7</mn></mrow><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mrow><mn>7</mn></mrow><mi>x</mi></mrow></mfenced><mo>-</mo><mfenced><mrow><mrow><mn>6</mn></mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mrow><mn>3</mn></mrow><mi>x</mi></mrow></mfenced></math>?</p>","rationale_html":"<p>Choice A is correct. Applying the distributive property, the given expression can be written as <math alttext=\"7 x cubed plus 7 x minus 6 x cubed plus 3 x\"><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>7</mn><mi>x</mi><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi></math>. Grouping like terms in this expression yields <math alttext=\"left parenthesis 7 x cubed minus 6 x cubed right parenthesis plus left parenthesis 7 x plus 3 x right parenthesis\"><mfenced><mrow><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>6</mn><msup><mi>x</mi><mn>3</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mrow><mn>7</mn><mi>x</mi><mo>+</mo><mn>3</mn><mi>x</mi></mrow></mfenced></math>. Combining like terms in this expression yields <math alttext=\"x cubed plus 10 x\"><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>10</mn><mi>x</mi></math>.</p>\n<p>Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice C is incorrect and may result from conceptual or calculation errors.</p>\n<p>Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["A"],"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=\"x cubed plus 10 x\"><mrow>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>3</mn>\n\t</msup>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>10</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"minus 13 x cubed plus 10 x\"><mrow>\n\t<mrow>\n\t\t<mo>-</mo>\n\t\t<mn>13</mn>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>3</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>10</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"minus 13 x cubed plus 4 x\"><mrow>\n\t<mrow>\n\t\t<mo>-</mo>\n\t\t<mn>13</mn>\n\t\t<msup>\n\t\t\t<mi>x</mi>\n\t\t\t<mn>3</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>x</mi>\n\t</mrow>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"x cubed plus 4 x\"><mrow>\n\t<msup>\n\t\t<mi>x</mi>\n\t\t<mn>3</mn>\n\t</msup>\n\t<mo>+</mo>\n\t<mrow>\n\t\t<mn>4</mn>\n\t\t<mi>x</mi>\n\t</mrow>\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}}