Algebraic Identities (6 and 7)

<p><a href="https://www.prepswift.com/quizzes/quiz/prepswift-algebraic-identities-6-and-7" target="_blank">Algebraic Identities (6 and 7) Exercise</a></p> <p><strong>Note</strong>: at about 1:19 into the video, it says that</p> <p>(2z + 4)<sup>3</sup>&nbsp;= 8z<sup>3</sup>&nbsp;+ 16z<sup>2</sup>&nbsp;+ 96zy<sup>2</sup>&nbsp;+ 64</p> <p>It should be (corrections have been bolded)</p> <p>(2z + 4)<sup>3</sup>&nbsp;= 8z<sup>3</sup>&nbsp;+ <strong>48</strong>z<sup>2</sup>&nbsp;+ 96<strong>z</strong> + 64</p><p>The &quot;algebraicians&quot; have extended their kindness, giving us 2 more nifty &quot;identities&quot;, this time to deal with cubes:</p> <p>Identity 6: <strong>$(x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3$</strong></p> <ul> <li>$(2 + 3)^3 = 2^3 + 3(2^2)(3) + 3(2)(3^2) + 3^3 = 8 + 54 + 18 + 27 = 125$</li> </ul> <p>Identity 7: <strong>$(x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3$</strong></p> <ul> <li>$(3 - 1)^3 = 3^3 - 3(3^2)(1) + 3(3)(1^2) - 1^3 = 27 - 27 + 9 - 1 = 8$</li> </ul> <p>It&#39;s worth noting that these rarely come up, but it&#39;s always good to be prepared!</p>