Hướng dẫn giải Bài 7 (Trang 8 SGK Toán Đại số 8, Tập 1)

Làm tính nhân: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>5</mn><mo>-</mo><mi>x</mi></mrow></mfenced></math> Từ câu b), hãy suy ra kết quả phép nhân: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced></math> Giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>.</mo><mi>x</mi><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>.</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mo>.</mo><mi>x</mi><mo>+</mo><mfenced><mrow><mo>-</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mo>.</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mo>+</mo><mn>1</mn><mo>.</mo><mi>x</mi><mo>+</mo><mn>1</mn><mo>.</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>3</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>1</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>5</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>3</mn></msup><mo>.</mo><mn>5</mn><mo>+</mo><msup><mi>x</mi><mn>3</mn></msup><mo>.</mo><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mo>.</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup></mrow></mfenced><mo>.</mo><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mi>x</mi><mo>.</mo><mn>5</mn><mo>+</mo><mi>x</mi><mo>.</mo><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mo>+</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mn>5</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfenced><mo>.</mo><mfenced><mrow><mo>-</mo><mi>x</mi></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><mn>5</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>10</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>5</mn><mi>x</mi><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>5</mn><mo>+</mo><mi>x</mi><mspace linebreak="newline"/><mo>=</mo><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>11</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>5</mn></math> Suy ra kết quả của phép nhân: <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mo>-</mo><mfenced><mrow><mn>5</mn><mo>-</mo><mi>x</mi></mrow></mfenced></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><mo>-</mo><mfenced><mrow><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>2</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mfenced><mrow><mn>5</mn><mo>-</mo><mi>x</mi></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><mo>-</mo><mfenced><mrow><mo>-</mo><msup><mi>x</mi><mn>4</mn></msup><mo>+</mo><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>-</mo><mn>11</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mo>-</mo><mn>5</mn></mrow></mfenced><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>4</mn></msup><mo>-</mo><mn>7</mn><msup><mi>x</mi><mn>3</mn></msup><mo>+</mo><mn>11</mn><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>6</mn><mi>x</mi><mo>+</mo><mn>5</mn></math>