{"id":"cb_question_bank:c502da97-d905-4ce0-bec6-a35eefd96b1b","source_id":"cb_question_bank","source_item_id":"c502da97-d905-4ce0-bec6-a35eefd96b1b","external_id":"4374fa03-6222-4e03-a842-f2d7a77397bb","ibn":null,"question_id":"d9137a84","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 represents the product of left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis and left parenthesis x Superscript 4 Baseline z Superscript 5 Baseline plus y Superscript 8 Baseline z Superscript negative 7 Baseline right parenthesis ?","stimulus":"","stimulus_html":null,"stem_html":"<p style=\"text-align: left;\">Which expression represents the product of&nbsp;<math alttext=\"left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mrow><mo>-</mo><mrow><mn>6</mn></mrow></mrow></msup><msup><mi>y</mi><mrow><mn>3</mn></mrow></msup><msup><mi>z</mi><mrow><mn>5</mn></mrow></msup></mrow></mfenced></math> and&nbsp;<math alttext=\"left parenthesis x Superscript 4 Baseline z Superscript 5 Baseline plus y Superscript 8 Baseline z Superscript negative 7 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mrow><mn>4</mn></mrow></msup><msup><mi>z</mi><mrow><mn>5</mn></mrow></msup><mo>+</mo><msup><mi>y</mi><mrow><mn>8</mn></mrow></msup><msup><mi>z</mi><mrow><mo>-</mo><mrow><mn>7</mn></mrow></mrow></msup></mrow></mfenced></math>?</p>","rationale_html":"<p style=\"text-align: left;\">Choice D is correct. The product of&nbsp;<math alttext=\"left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>5</mn></msup></mrow></mfenced></math> and&nbsp;<math alttext=\"left parenthesis x Superscript 4 Baseline z Superscript 5 Baseline plus y Superscript 8 Baseline z Superscript negative 7 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><msup><mi>z</mi><mn>5</mn></msup><mo>+</mo><msup><mi>y</mi><mn>8</mn></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>7</mn></mrow></msup></mrow></mfenced></math> can be represented by the expression&nbsp;<math alttext=\"left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis left parenthesis x Superscript 4 Baseline z Superscript 5 Baseline plus y Superscript 8 Baseline z Superscript negative 7 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>5</mn></msup></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><msup><mi>z</mi><mn>5</mn></msup><mo>+</mo><msup><mi>y</mi><mn>8</mn></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>7</mn></mrow></msup></mrow></mfenced></math>. Applying the distributive property to this expression yields&nbsp;<math alttext=\"left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis left parenthesis x Superscript 4 Baseline z Superscript 5 Baseline right parenthesis plus left parenthesis x Superscript negative 6 Baseline y cubed z Superscript 5 Baseline right parenthesis left parenthesis y Superscript 8 Baseline z Superscript negative 7 Baseline right parenthesis\"><mfenced><mrow><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>5</mn></msup></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>4</mn></msup><msup><mi>z</mi><mn>5</mn></msup></mrow></mfenced><mo>+</mo><mfenced><mrow><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>5</mn></msup></mrow></mfenced><mfenced><mrow><msup><mi>y</mi><mn>8</mn></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>7</mn></mrow></msup></mrow></mfenced></math>, or&nbsp;<math alttext=\"x Superscript negative 6 Baseline x Superscript 4 Baseline y cubed z Superscript 5 Baseline z Superscript 5 plus x Superscript negative 6 Baseline y cubed y Superscript 8 Baseline z Superscript 5 Baseline z Superscript negative 7\"><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>x</mi><mn>4</mn></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>5</mn></msup><msup><mi>z</mi><mn>5</mn></msup><mo>+</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>y</mi><mn>8</mn></msup><msup><mi>z</mi><mn>5</mn></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>7</mn></mrow></msup></math>. This expression is equivalent to&nbsp;<math alttext=\"x Superscript negative 6 plus 4 Baseline y cubed z Superscript 5 plus 5 plus x Superscript negative 6 Baseline y Superscript 3 plus 8 Baseline z Superscript 5 minus 7\"><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn><mo>+</mo><mn>4</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mrow><mn>5</mn><mo>+</mo><mn>5</mn></mrow></msup><mo>+</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mrow><mn>3</mn><mo>+</mo><mn>8</mn></mrow></msup><msup><mi>z</mi><mrow><mn>5</mn><mo>-</mo><mn>7</mn></mrow></msup></math>, or&nbsp;<math alttext=\"x Superscript negative 2 Baseline y cubed z Superscript 10 plus x Superscript negative 6 Baseline y Superscript 11 Baseline z Superscript negative 2\"><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mi>y</mi><mn>3</mn></msup><msup><mi>z</mi><mn>10</mn></msup><mo>+</mo><msup><mi>x</mi><mrow><mo>-</mo><mn>6</mn></mrow></msup><msup><mi>y</mi><mn>11</mn></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></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 C is incorrect and may result from conceptual or calculation errors.</p>","correct_answer":["D"],"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 Superscript negative 2 Baseline z Superscript 10 plus y Superscript 11 Baseline z Superscript negative 2\"><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mi>z</mi><mrow><mn>10</mn></mrow></msup><mo>+</mo><msup><mi>y</mi><mrow><mn>11</mn></mrow></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>","ord":0},{"label":"B","content_html":"<p><math alttext=\"x Superscript negative 2 Baseline z Superscript 10 plus x Superscript negative 6 Baseline z Superscript negative 2\"><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mi>z</mi><mrow><mn>10</mn></mrow></msup><mo>+</mo><msup><mi>x</mi><mrow><mo>-</mo><mrow><mn>6</mn></mrow></mrow></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></math></p>","ord":1},{"label":"C","content_html":"<p><math alttext=\"x Superscript negative 2 Baseline y cubed z Superscript 10 plus y Superscript 8 Baseline z Superscript negative 7\"><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mi>y</mi><mrow><mn>3</mn></mrow></msup><msup><mi>z</mi><mrow><mn>10</mn></mrow></msup><mo>+</mo><msup><mi>y</mi><mrow><mn>8</mn></mrow></msup><msup><mi>z</mi><mrow><mo>-</mo><mrow><mn>7</mn></mrow></mrow></msup></math></p>","ord":2},{"label":"D","content_html":"<p><math alttext=\"x Superscript negative 2 Baseline y cubed z Superscript 10 plus x Superscript negative 6 Baseline y Superscript 11 Baseline z Superscript negative 2\"><msup><mi>x</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup><msup><mi>y</mi><mrow><mn>3</mn></mrow></msup><msup><mi>z</mi><mrow><mn>10</mn></mrow></msup><mo>+</mo><msup><mi>x</mi><mrow><mo>-</mo><mrow><mn>6</mn></mrow></mrow></msup><msup><mi>y</mi><mrow><mn>11</mn></mrow></msup><msup><mi>z</mi><mrow><mo>-</mo><mn>2</mn></mrow></msup></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}}