Bài 3: Hằng đẳng thức đáng nhớ
Khám phá 4 trang 21 Toán 8 tập 1
<p><strong>Kh&aacute;m ph&aacute; 4 trang 21 To&aacute;n 8 Tập 1:&nbsp;</strong>Sử dụng quy tắc chuyển vế v&agrave; c&aacute;c t&iacute;nh chất của ph&eacute;p to&aacute;n, ho&agrave;n th&agrave;nh c&aacute;c biến đổi sau v&agrave;o vở:</p> <div class="ads_ads ads_1"><ins class="adsbygoogle" data-ad-client="ca-pub-2373417360267295" data-ad-slot="9405778504" data-ad-format="auto" data-full-width-responsive="true" data-adsbygoogle-status="done" data-ad-status="unfilled"> <div id="aswift_1_host" tabindex="0" title="Advertisement" aria-label="Advertisement"></div> </ins></div> <p>(a + b)<sup>3</sup>&nbsp;= a<sup>3</sup>&nbsp;+ 3a<sup>2</sup>b + 3ab<sup>2</sup>&nbsp;+ b<sup>3</sup></p> <p>a<sup>3</sup>&nbsp;+ b<sup>3</sup>&nbsp;= (a + b)<sup>3</sup>&nbsp;&ndash; 3a<sup>2</sup>b &ndash; 3ab<sup>2</sup></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)<sup>3</sup>&nbsp;&ndash; 3ab(a + b)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)(&hellip;)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = &hellip;</p> <p>(a &ndash; b)<sup>3</sup>&nbsp;= a<sup>3</sup>&nbsp;&ndash; 3a<sup>2</sup>b + 3ab<sup>2</sup>&nbsp;&ndash; b<sup>3</sup></p> <p>a<sup>3</sup>&nbsp;&ndash; b<sup>3</sup>&nbsp;= (a &ndash; b)<sup>3</sup>&nbsp;+ 3a<sup>2</sup>b &ndash; 3ab<sup>2</sup></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a &ndash; b)<sup>3</sup>&nbsp;+ 3ab(a &ndash; b)</p> <p>&nbsp;&nbsp; &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;= (a &ndash; b)(&hellip;)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = &hellip;</p> <p><strong>Lời giải:</strong></p> <p>(a + b)<sup>3</sup>&nbsp;= a<sup>3</sup>&nbsp;+ 3a<sup>2</sup>b + 3ab<sup>2</sup>&nbsp;+ b<sup>3</sup></p> <p>a<sup>3</sup>&nbsp;+ b<sup>3</sup>&nbsp;= (a + b)<sup>3</sup>&nbsp;&ndash; 3a<sup>2</sup>b &ndash; 3ab<sup>2</sup></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)<sup>3</sup>&nbsp;&ndash; 3ab(a + b)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)[(a + b)<sup>2</sup>&nbsp;&ndash; 3ab]</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)(a<sup>2</sup>&nbsp;+ 2ab + b<sup>2</sup>&nbsp;&ndash; 3ab)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a + b)(a<sup>2</sup>&nbsp;&ndash; ab + b<sup>2</sup>).</p> <p>(a &ndash; b)<sup>3</sup>&nbsp;= a<sup>3</sup>&nbsp;&ndash; 3a<sup>2</sup>b + 3ab<sup>2</sup>&nbsp;&ndash; b<sup>3</sup></p> <p>a<sup>3</sup>&nbsp;&ndash; b<sup>3</sup>&nbsp;= (a &ndash; b)<sup>3</sup>&nbsp;+ 3a<sup>2</sup>b &ndash; 3ab<sup>2</sup></p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a &ndash; b)<sup>3</sup>&nbsp;+ 3ab(a &ndash; b)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a &ndash; b)[(a &ndash; b)<sup>2</sup>&nbsp;+ 3ab]</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a &ndash; b)(a<sup>2</sup>&nbsp;&ndash; 2ab + b<sup>2</sup>&nbsp;+ 3ab)</p> <p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; = (a &ndash; b)(a<sup>2</sup>&nbsp;+ ab + b<sup>2</sup>).</p>
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