Bài 26: Phép cộng và phép trừ đa thức một biến
Hướng dẫn giải Bài 7.14 (Trang 33 SGK Toán 7, Bộ Kết nối tri thức, Tập 2)
<p><strong>B&agrave;i 7.14 (Trang 33 SGK To&aacute;n lớp 7 - Bộ Kết nối tri thức với cuộc sống, Tập 2):</strong></p> <p>Cho hai đa thức:</p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p> <p>T&iacute;nh A + B v&agrave; A - B.</p> <p><strong><em>Hướng dẫn giải:</em></strong></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">A</mi><mo mathvariant="bold">&#160;</mo><mo mathvariant="bold">+</mo><mo mathvariant="bold">&#160;</mo><mi mathvariant="bold-italic">B</mi><mo>&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mfenced><mrow><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mo>(</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>)</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mo>(</mo><mo>-</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>)</mo><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mo>(</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>)</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math></p> <p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="bold-italic">A</mi><mo mathvariant="bold">&#160;</mo><mo mathvariant="bold">-</mo><mo mathvariant="bold">&#160;</mo><mi mathvariant="bold-italic">B</mi><mo mathvariant="bold">&#160;</mo><mo>=</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfenced><mrow><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#8201;</mo><mi>x</mi><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mo>(</mo><mn>6</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>3</mn><msup><mi>x</mi><mn>4</mn></msup><mo>)</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mo>(</mo><mo>-</mo><mn>4</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>)</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mo>(</mo><mi>x</mi><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mi>x</mi><mo>)</mo><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mfenced><mrow><mo>-</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></mrow></mfenced></math></p> <p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>&#160;</mo><mn>9</mn><msup><mi>x</mi><mn>4</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>&#160;</mo><mo>+</mo><mo>&#160;</mo><mn>5</mn><msup><mi>x</mi><mn>2</mn></msup><mo>&#160;</mo><mo>-</mo><mo>&#160;</mo><mn>1</mn></math></p>
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