Hướng dẫn Giải Bài 55 (trang 30, SGK Toán 9, Tập 1)

Hướng dẫn giải Bài 55 (Trang 30 SGK Toán 9, Tập 1)

Bài 55 (Trang 30 SGK Toán 9, Tập 1): Phân tích thành nhân tử (với a, b, x, y là các số không âm). a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>;</mo></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">y</mi><mn>3</mn></msup></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mi mathvariant="normal">y</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi>xy</mi><mn>2</mn></msup></msqrt><mo>.</mo></math>   Hướng dẫn giải: a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mfenced open="[" close="]"><mrow><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mi mathvariant="normal">b</mi><mo> </mo><mo>+</mo><mo> </mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt></mrow></mfenced><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo></math>    <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mo> </mo><mo>+</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mo>(</mo><mi mathvariant="normal">b</mi><msqrt><mi mathvariant="normal">a</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>1</mn><mo>)</mo><mo>;</mo></math> b) <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><msup><mi mathvariant="normal">x</mi><mn>3</mn></msup></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">y</mi><mn>3</mn></msup></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mi mathvariant="normal">y</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi>xy</mi><mn>2</mn></msup></msqrt><mo> </mo><mo>=</mo><mo> </mo><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>)</mo></mrow><mn>3</mn></msup><mo> </mo><mo>-</mo><mo> </mo><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></mrow><mn>3</mn></msup><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mi mathvariant="normal">y</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><msup><mi>xy</mi><mn>2</mn></msup></msqrt></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>(</mo><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>xy</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></msqrt><mo>)</mo><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi>xy</mi></msqrt><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>(</mo><msqrt><msup><mi mathvariant="normal">x</mi><mn>2</mn></msup><mo> </mo></msqrt><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mi>xy</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><msup><mi mathvariant="normal">y</mi><mn>2</mn></msup></msqrt><mo>)</mo></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mfenced open="[" close="]"><mrow><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo> </mo><mo>+</mo><mo> </mo><mn>2</mn><msqrt><mi mathvariant="normal">x</mi></msqrt><msqrt><mi mathvariant="normal">y</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup></mrow></mfenced></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><msup><mrow><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></mrow><mn>2</mn></msup><mo> </mo><mo>=</mo><mo> </mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>-</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>.</mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>.</mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo> </mo><mo>+</mo><mo> </mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo></math>   <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">x</mi><mo>-</mo><mi mathvariant="normal">y</mi><mo>)</mo><mo>(</mo><msqrt><mi mathvariant="normal">x</mi></msqrt><mo>+</mo><msqrt><mi mathvariant="normal">y</mi></msqrt><mo>)</mo><mo>.</mo></math>