{"id":"cb_question_bank:39d2f131-473f-46e5-9430-248847032ef1","source_id":"cb_question_bank","source_item_id":"39d2f131-473f-46e5-9430-248847032ef1","external_id":"a81bca68-7fa7-4265-906c-6d5f61769b51","ibn":null,"question_id":"5b6af6b1","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 d minus 6 right parenthesis left parenthesis 8 d squared minus 3 right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression is equivalent to&nbsp;<math alttext=\"left parenthesis d minus 6 right parenthesis left parenthesis 8 d squared minus 3 right parenthesis\"><mfenced><mrow><mi>d</mi><mo>-</mo><mrow><mn>6</mn></mrow></mrow></mfenced><mfenced><mrow><mrow><mn>8</mn></mrow><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mrow><mn>3</mn></mrow></mrow></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice C is correct. Applying the distributive property to the given expression yields&nbsp;<math alttext=\"d left parenthesis 8 d squared minus 3 right parenthesis minus 6 left parenthesis 8 d squared minus 3 right parenthesis\"><mi>d</mi><mfenced><mrow><mn>8</mn><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow></mfenced><mo>-</mo><mn>6</mn><mfenced><mrow><mn>8</mn><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow></mfenced></math>. Applying the distributive property once again to this expression yields <math alttext=\"left parenthesis d right parenthesis left parenthesis 8 d squared right parenthesis plus left parenthesis d right parenthesis left parenthesis negative 3 right parenthesis plus left parenthesis negative 6 right parenthesis left parenthesis 8 d squared right parenthesis plus left parenthesis negative 6 right parenthesis left parenthesis negative 3 right parenthesis\"><mfenced><mi>d</mi></mfenced><mfenced><mrow><mn>8</mn><msup><mi>d</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mi>d</mi></mfenced><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced><mfenced><mrow><mn>8</mn><msup><mi>d</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfenced><mfenced><mrow><mo>-</mo><mn>3</mn></mrow></mfenced></math>, or <math alttext=\"8 d cubed plus left parenthesis minus 3 d right parenthesis plus left parenthesis minus 48 d squared right parenthesis plus 18\"><mn>8</mn><msup><mi>d</mi><mn>3</mn></msup><mo>+</mo><mfenced><mrow><mo>-</mo><mn>3</mn><mi>d</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>48</mn><msup><mi>d</mi><mn>2</mn></msup></mrow></mfenced><mo>+</mo><mn>18</mn></math>. This expression can be rewritten as <math alttext=\"8 d cubed minus 48 d squared minus 3 d plus 18\"><mn>8</mn><msup><mi>d</mi><mn>3</mn></msup><mo>-</mo><mn>48</mn><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>d</mi><mo>+</mo><mn>18</mn></math>. Thus,&nbsp;<math alttext=\"left parenthesis d minus 6 right parenthesis left parenthesis 8 d squared minus 3 right parenthesis\"><mfenced><mrow><mi>d</mi><mo>-</mo><mn>6</mn></mrow></mfenced><mfenced><mrow><mn>8</mn><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn></mrow></mfenced></math> is equivalent to <math alttext=\"8 d cubed minus 48 d squared minus 3 d plus 18\"><mn>8</mn><msup><mi>d</mi><mn>3</mn></msup><mo>-</mo><mn>48</mn><msup><mi>d</mi><mn>2</mn></msup><mo>-</mo><mn>3</mn><mi>d</mi><mo>+</mo><mn>18</mn></math>.</p>\n<p style=\"text-align: left;\">Choice A is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice B is incorrect and may result from conceptual or calculation errors.</p>\n<p style=\"text-align: left;\">Choice D is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["C"],"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=\"8 d cubed minus 14 d squared minus 3 d plus 18\"><mrow>\n\t<mrow>\n\t\t<mn>8</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>14</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>3</mn>\n\t\t<mi>d</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>18</mn>\n</mrow>\n</math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"8 d cubed minus 17 d squared plus 48\"><mrow>\n\t<mrow>\n\t\t<mn>8</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>17</mn>\n\t\t<msup>\n\t\t\t<mi>d</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>48</mn>\n</mrow>\n</math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"8 d cubed minus 48 d squared minus 3 d plus 18\"><mrow>\n\t<mrow>\n\t\t<mn>8</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>48</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>3</mn>\n\t\t<mi>d</mi>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>18</mn>\n</mrow>\n</math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"8 d cubed minus 51 d squared plus 48\"><mrow>\n\t<mrow>\n\t\t<mn>8</mn>\n\t\t<msup>\n\t\t\t<mi>d</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>51</mn>\n\t\t<msup>\n\t\t\t<mi>d</mi>\n\t\t\t<mn>2</mn>\n\t\t</msup>\n\t</mrow>\n\t<mo>+</mo>\n\t<mn>48</mn>\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}}