Bài 7: Phân Tích Đa Thức Thành Nhân Tử Bằng Phương Pháp Dùng Hằng Đẳng Thức
Hướng dẫn giải Bài 44 (Trang 20 SGK Toán Đại số 8, Tập 1)
<p>Phân tích các đa thức sau thành nhân tử:</p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>27</mn></mfrac><mo>;</mo><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>;</mo><mo> </mo><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>;</mo><mspace linebreak="newline"/><mi>d</mi><mo>)</mo><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mi>y</mi><mo>+</mo><mn>6</mn><mi>x</mi><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup><mo>;</mo><mspace linebreak="newline"/><mi>e</mi><mo>)</mo><mo>−</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>27</mn><mi>x</mi><mo>+</mo><mn>27</mn><mo>;</mo></math></p>
<p><strong>Giải:</strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mfrac><mn>1</mn><mn>27</mn></mfrac><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi><mo>.</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>3</mn></mfrac></mfenced><mn>2</mn></msup></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><mfenced><mrow><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></mrow></mfenced><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>9</mn></mfrac></mrow></mfenced></math></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>.</mo><mo> </mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>−</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><mo>[</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>−</mo><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo><mo>]</mo><mo>[</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>+</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>.</mo><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo><mo>+</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>]</mo><mo> </mo><mspace linebreak="newline"/><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>−</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo><mspace linebreak="newline"/><mo>=</mo><mn>2</mn><mi>b</mi><mo>(</mo><mn>3</mn><msup><mi>a</mi><mn>3</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo></math></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>.</mo><mo> </mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>+</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><mo>[</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo><mo>]</mo><mo>[</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>−</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo><mo>+</mo><msup><mrow><mo>(</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>]</mo><mo> </mo><mspace linebreak="newline"/><mo>=</mo><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>a</mi><mo>−</mo><mi>b</mi><mo>)</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a</mi><mn>2</mn></msup><mo>−</mo><mn>2</mn><mi>a</mi><mi>b</mi><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup><mo>]</mo><mspace linebreak="newline"/><mo>=</mo><mn>2</mn><mi>a</mi><mo>.</mo><mo>(</mo><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><msup><mi>b</mi><mn>2</mn></msup><mo>)</mo></math></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>)</mo><mn>8</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>12</mn><msup><mi>x</mi><mn>2</mn></msup><mi>y</mi><mo>+</mo><mn>6</mn><mi>x</mi><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mn>3</mn></msup><mo>+</mo><mn>3</mn><mo>.</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>)</mo></mrow><mn>2</mn></msup><mo>.</mo><mi>y</mi><mo>+</mo><mn>3</mn><mo>.</mo><mn>2</mn><mi>x</mi><mo>.</mo><mi>y</mi><mo>+</mo><msup><mi>y</mi><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mrow><mo>(</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>y</mi><mo>)</mo></mrow><mn>3</mn></msup></math></strong></p>
<p><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>)</mo><mo>−</mo><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mn>27</mn><mi>x</mi><mo>+</mo><mn>27</mn><mspace linebreak="newline"/><mo>=</mo><mn>27</mn><mo>−</mo><mn>27</mn><mi>x</mi><mo>+</mo><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>x</mi><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mn>3</mn><mn>3</mn></msup><mo>−</mo><mn>3</mn><mo>.</mo><msup><mn>3</mn><mn>2</mn></msup><mo>.</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>.</mo><mn>3</mn><mo>.</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><msup><mi>x</mi><mn>3</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mrow><mo>(</mo><mn>3</mn><mo>−</mo><mi>x</mi><mo>)</mo></mrow><mn>3</mn></msup></math></strong></p>
Hướng dẫn Giải Bài 44 (Trang 20, SGK Toán 8, Tập 1)
GV: 
GV colearn
GV colearn
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Hướng dẫn Giải Bài 44 (Trang 20, SGK Toán 8, Tập 1)
GV: GV colearn
GV colearn