{"id":"act_quizme:math:q3:01","source_id":"act_quizme","source_item_id":"math-q3-01","external_id":"371426efaa8aa0bc","program":"ACT","section":"math","category_code":null,"category":null,"subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":1,"scored":true,"layout_warning":null,"stem":"Which of the following expressions is equivalent to (y+7) cubed ( y + 7 ) 3 ?","stimulus":"","stimulus_html":null,"stem_html":"<div class=\"math-question-wrap\"> <p>Which of the following expressions is equivalent to <span style=\"white-space: nowrap;\"><span class=\"visually-hidden\">(y+7) cubed</span><math class=\"srTransform\"> <msup> <mrow> <mo>(</mo> <mi>y</mi> <mo>+</mo> <mn>7</mn> <mo>)</mo> </mrow> <mn>3</mn> </msup> </math>?</span></p> </div> <div> <div class=\"math-answer-select-wrap\"> </div></div>","rationale_html":"<p><strong>A.</strong> <strong>Correct.</strong> Rewrite the expression without exponents: <span style=\"white-space: nowrap;\"><math><msup><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mn>3</mn></msup><mo>=</mo><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>.</span> Multiply the first <span style=\"white-space: nowrap;\"><math><mn>2</mn></math>&nbsp;binomials:</span> <span style=\"white-space: nowrap;\"><math><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mo>=</mo><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>.</span> Then, multiply the trinomial&nbsp;<math><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced></math>&nbsp;by the binomial&nbsp;<math><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>&nbsp;using the distributive property: <span style=\"white-space: nowrap;\"><math><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mo>=</mo><mi>y</mi><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced><mo>+</mo><mn>7</mn><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced></math>.</span> Expand the expression and combine like terms: <span style=\"white-space: nowrap;\"><math><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>14</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>49</mn><mi>y</mi><mo>+</mo><mn>7</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>98</mn><mi>y</mi><mo>+</mo><mn>343</mn><mo>=</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>21</mn><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>147</mn><mi>y</mi><mo>+</mo><mn>343</mn></math>.</span><span style=\"white-space: nowrap;\">&nbsp;</span></p><p><strong>B.</strong> <strong>Incorrect. </strong>You may have correctly derived the expression <span style=\"white-space: nowrap;\"><math><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>,</span> but instead of multiplying the binomial by the trinomial, you may have multiplied&nbsp;<math><mi>y</mi></math>&nbsp;by only&nbsp;<math><msup><mi>y</mi><mn>2</mn></msup></math>&nbsp;and&nbsp;<math><mn>7</mn></math>&nbsp;by only&nbsp;<math><mn>49</mn></math>&nbsp;to get <span style=\"white-space: nowrap;\">&nbsp;<math><mi>y</mi><mfenced><msup><mi>y</mi><mn>2</mn></msup></mfenced><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>7</mn><mfenced><mn>49</mn></mfenced><mo>=</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>343</mn></math>.</span> Be sure to use the distributive property correctly and combine like terms.</p><p><strong>C.</strong> <strong>Incorrect. </strong>You may have correctly derived the expression <span style=\"white-space: nowrap;\"><math><mfenced><mrow><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>,</span> but instead of multiplying the binomial by the trinomial, you may have multiplied the&nbsp;first term by only&nbsp;<math><mi>y</mi></math>&nbsp;to get <span style=\"white-space: nowrap;\"><math><mi>y</mi><mfenced><msup><mi>y</mi><mn>2</mn></msup></mfenced><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn><mo>=</mo><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>14</mn><mi>y</mi><mo>+</mo><mn>49</mn></math>.</span> Be sure to use the distributive property and combine like terms.</p><p><strong>D.</strong> <strong>Incorrect. </strong>You may have cubed the&nbsp;<math><mi>y</mi></math>&nbsp;and the&nbsp;<math><mn>7</mn></math>&nbsp;and then added the results to get <span style=\"white-space: nowrap;\"><math><msup><mi>y</mi><mn>3</mn></msup><mo>+</mo><mn>343</mn></math>.</span> Instead, rewrite the expression without exponents: <span style=\"white-space: nowrap;\"><math><msup><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mn>3</mn></msup><mo>=</mo><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced><mfenced><mrow><mi>y</mi><mo>+</mo><mn>7</mn></mrow></mfenced></math>.</span> Then, use the distributive property to expand the expression and combine like terms.</p>","correct_answer":["A"],"equiv_key":"b4f57a7311d404f5b079456d","has_media":false,"has_mathml":true,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p><span>y cubed +21y squared +147y+343</span> y 3 + 21 y 2 + 147 y + 343</p>","ord":0},{"label":"B","content_html":"<p><span>y cubed +14y+343</span> y 3 + 14 y + 343</p>","ord":1},{"label":"C","content_html":"<p><span>y cubed +14y+49</span> y 3 + 14 y + 49</p>","ord":2},{"label":"D","content_html":"<p><span>y cubed +343</span> y 3 + 343</p>","ord":3}],"passage":null,"attribution":{"source_id":"act_quizme","source_name":"ACT QuizMe official practice questions","rights_holder":"ACT Education Corp.","canonical_url":"https://quizme.act.org/","retrieved_from":"https://quizme.act.org/","attribution":"Official ACT practice questions © ACT Education Corp., from the QuizMe practice quizzes at quizme.act.org.","disclaimer":"ACT® is a registered trademark of ACT Education Corp., which is not affiliated with, does not sponsor, and does not endorse this project.","license":"ACT Education Corp. copyright. 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