Hi there. In this math post I quickly cover the concept of difference of cubes. This is one of those niche math/algebra topics that comes up when it comes to simplifying algebra expressions. This topic is more for high school students in Grade 11 or 12 and for university students in engineering, math and maybe science students. <center><img src="https://cdn.pixabay.com/photo/2021/04/13/06/58/board-6174817_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2021/04/13/06/58/board-6174817_960_720.jpg">Image Source</a></center> ## The Formula --- For the difference of cubes you need to have an expression of the form: <center>https://quicklatex.com/cache3/d5/ql_8dd272bd5da2fd45cff85a2b4696b2d5_l3.png</center> then you can factor this difference of cubes into: <center>https://quicklatex.com/cache3/5f/ql_137e5bbe1d6c33b4892052d10bca875f_l3.png</center> **Variation - Sum of Cubes** A variation of the difference of cubes is factoring sum of cubes. <center>https://quicklatex.com/cache3/14/ql_74802c9f7e2f6c3959f1b4faa9605a14_l3.png</center> The `ab` term sign changes in this variation. It is `-ab`. <center><img src="https://cdn.pixabay.com/photo/2015/11/15/07/44/learn-1044076_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2015/11/15/07/44/learn-1044076_960_720.jpg">Image Source</a></center> ## Examples --- **Example One** Factor the difference of cubes https://quicklatex.com/cache3/17/ql_87fbae6e463e4720dffeea8f391bc917_l3.png In this case `x = a` and `b = 2` from b-cubed equal to 8. Apply the formula to get the factors. <center>https://quicklatex.com/cache3/68/ql_eb4aad8d88ab3eb31fad6357773e1a68_l3.png</center> **Example Two** Factor https://quicklatex.com/cache3/5a/ql_c03d31595248dfc05b2d36354f522f5a_l3.png. Here we have `x = a` and `y^2 = b`. Apply the formula accordingly. <center>https://quicklatex.com/cache3/30/ql_104390d998fddffeff1bdad95c0eaa30_l3.png</center> **Example Three** Simplify https://quicklatex.com/cache3/f9/ql_c4e3a6eaac92d5f4c0aab97f426917f9_l3.png. The top part of the fraction is a difference of cubes. Factoring the top may reveal something helpful for simplifying the fraction. On the top you have the cube root of x-cubed which is `x`. The cube root of 27 is 3. Apply the difference of cubes formula for the top. <center>https://quicklatex.com/cache3/f3/ql_94b4782cfe80baa1d1375095f4ba94f3_l3.png</center> You now have `(x - 3)` factors that can be cancelled on the top and bottom. <center>https://quicklatex.com/cache3/71/ql_8407863777b671e70cf197c25337f371_l3.png</center> The fraction simplifies into a quadratic expression. <center><img src="https://cdn.pixabay.com/photo/2016/08/26/15/20/mathematics-1622448_960_720.jpg" /></center> <center><a href="https://cdn.pixabay.com/photo/2016/08/26/15/20/mathematics-1622448_960_720.jpg">Image Source</a></center> <center>Thank you for reading.</center>
| author | dkmathstats |
|---|---|
| permlink | difference-of-two-cubes-math |
| category | hive-163521 |
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| created | 2024-10-12 23:43:21 |
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| okluvmee | 0 | 1,053,841,161 | 0.6% | ||
| holovision.cash | 0 | 2,524,391,196 | 100% | ||
| krrizjos18 | 0 | 4,400,003,075 | 50% | ||
| holovision.stem | 0 | 690,243,897 | 100% | ||
| hubeyma | 0 | 14,101,354,328 | 50% | ||
| lunasilver73 | 0 | 2,633,364,672 | 50% | ||
| lesliekat | 0 | 1,623,622,634 | 50% | ||
| sara-escribe | 0 | 1,421,459,398 | 50% | ||
| solominer.stem | 0 | 948,318,291 | 100% | ||
| irivers | 0 | 0 | 100% | ||
| gislandpoetic | 0 | 1,044,918,359 | 50% | ||
| iamleicester | 0 | 473,623,667 | 80% | ||
| tanzil2024 | 0 | 1,853,203,542 | 1% | ||
| aries90 | 0 | 11,703,804,504 | 1.2% | ||
| blingit | 0 | 782,459,449 | 0.6% | ||
| jrjaime | 0 | 17,111,454,797 | 100% | ||
| zirkonov | 0 | 1,215,432,889 | 30% | ||
| yixn | 0 | 2,894,741,673 | 0.6% | ||
| kqaosphreak | 0 | 763,455,482 | 10% | ||
| slaifer-red-01 | 0 | 1,571,888,315 | 50% | ||
| newilluminati | 0 | 3,573,264,446 | 0.6% | ||
| maca1803 | 0 | 1,345,492,170 | 100% | ||
| lichtkunstfoto | 0 | 1,647,170,641 | 1.2% | ||
| vindiesel1980 | 0 | 1,767,698,881 | 0.6% | ||
| netvalar | 0 | 22,618,199,119 | 50% | ||
| lukasbachofner | 0 | 981,219,481 | 0.6% | ||
| benwickenton | 0 | 578,363,284 | 1.2% | ||
| cryptocubangirl | 0 | 1,396,759,286 | 50% | ||
| jose-sw31 | 0 | 1,638,975,361 | 50% | ||
| azj26 | 0 | 4,690,328,157 | 16% | ||
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| neocientiacu | 0 | 561,750,050 | 100% | ||
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| llunasoul | 0 | 627,808,256 | 1.11% | ||
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| jijisaurart | 0 | 532,242,475 | 0.6% | ||
| clpacksperiment | 0 | 547,758,510 | 0.6% | ||
| humbe | 0 | 8,061,655,540 | 2% | ||
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| adotours | 0 | 2,086,591,544 | 100% | ||
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<p><strong>¡Felicitaciones!</strong></p><hr /><div class="text-center"><img src="https://steemitimages.com/0x0/https://s7.postimg.cc/wif5wzgbv/finnalcoment.png" alt="Has sido votado por @entropia"/></div><hr /><div class="text-justify"><p>Estás participando para optar a la <b>mención especial</b> que se efectuará el domingo 20 de octubre del 2024 a las 8:00 pm (hora de Venezuela), gracias a la cual el autor del artículo seleccionado recibirá la cantidad de 1 HIVE transferida a su cuenta.</p><p>¡También has recibido <b>1 ENTROKEN</b>! El <a href="https://hive.blog/entropia/@entropia/enhorabuena-estamos-de-aniversario-y-anunciamos-oficialmente-el-lanzamiento-de-entroken-entro-un-nuevo-token-una-nueva">token del PROYECTO ENTROPÍA</a> impulsado por la plataforma <a href="https://steem-engine.com/">Steem-Engine.</a></p></div><hr /><div class="text-justify"><p>1. <b>Invierte en el PROYECTO ENTROPÍA y recibe ganancias semanalmente</b>. Entra <a href='https://hive.blog/entropia/@entropia/nm7zz-invierte-en-entropia-y-obten-un-10-95-de-ganancia-de-tu-delegacion-de-hive-power-recibiendo-tu-pago-de-forma-automatica'>aquí</a> para más información.</p><p>2. Contáctanos en Discord: <a href='https://discord.gg/hkCjFeb' rel='noopener' title='This link will take you away from hive.blog'>https://discord.gg/hkCjFeb</a></p><p>3. Suscríbete a nuestra <a href='https://hive.blog/trending/hive-180318'>COMUNIDAD</a> y apoya al trail de @Entropia y así podrás ganar recompensas de curación de forma automática. <a href='https://hive.blog/entropia/@entropia/3kq4ti-gana-recompensas-de-curacion-de-forma-automatica-con-nosotros-unete-al-trail-del-proyecto-entropia'>Entra aquí para más información sobre nuestro trail</a>.</p><p>4. Visita nuestro canal de <a href='https://www.youtube.com/channel/UCJI9zlYwJMQ4NlFUbBR0-pw'>Youtube</a>.</p></div><div class='text-center'><p>Atentamente</p><p><strong><em>El equipo de curación del PROYECTO ENTROPÍA</em></strong></p></div>
| author | entropia |
|---|---|
| permlink | re-difference-of-two-cubes-math-20241014t024847z |
| category | hive-163521 |
| json_metadata | "{"app": "beem/0.24.26"}" |
| created | 2024-10-14 02:48:48 |
| last_update | 2024-10-14 02:48:48 |
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| root_title | "Difference Of Two Cubes [Math, Algebra]" |
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<div class='text-justify'> <div class='pull-left'> <img src='https://stem.openhive.network/images/stemsocialsupport7.png'> </div> Thanks for your contribution to the <a href='/trending/hive-196387'>STEMsocial community</a>. Feel free to join us on <a href='https://discord.gg/9c7pKVD'>discord</a> to get to know the rest of us! Please consider delegating to the @stemsocial account (85% of the curation rewards are returned). You may also include @stemsocial as a beneficiary of the rewards of this post to get a stronger support. <br /> <br /> </div>
| author | stemsocial |
|---|---|
| permlink | re-dkmathstats-difference-of-two-cubes-math-20241013t045936841z |
| category | hive-163521 |
| json_metadata | {"app":"STEMsocial"} |
| created | 2024-10-13 04:59:36 |
| last_update | 2024-10-13 04:59:36 |
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| root_title | "Difference Of Two Cubes [Math, Algebra]" |
| beneficiaries | [] |
| max_accepted_payout | 1,000,000.000 HBD |
| percent_hbd | 10,000 |
| post_id | 137,826,520 |
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