Hướng dẫn giải Bài 16 (Trang 11 SGK Toán Đại số 8, Tập 1)

Viết các biểu thức sau dưới dạng bình phương của một tổng hoặc một hiệu: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mo>)</mo><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><mo>(</mo><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mi>y</mi><mo>)</mo><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>)</mo><mo> </mo><mo>(</mo><mn>25</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><mi>a</mi><mi>b</mi><mo>)</mo><mo>;</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>)</mo><mo> </mo><mo>(</mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>)</mo><mo>;</mo></math> Giải: <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mi>x</mi><mo>+</mo><mn>1</mn><mspace linebreak="newline"/><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>.</mo><mi>x</mi><mo>.</mo><mn>1</mn><mo>+</mo><msup><mn>1</mn><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>+</mo><mn>1</mn></mrow></mfenced><mn>2</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>)</mo><mo> </mo><mn>9</mn><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>+</mo><mn>6</mn><mi>x</mi><mi>y</mi><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>3</mn><mi>x</mi></mrow></mfenced><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>.</mo><mn>3</mn><mo>.</mo><mi>x</mi><mo>.</mo><mi>y</mi><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>3</mn><mi>x</mi><mo>+</mo><mi>y</mi></mrow></mfenced><mn>2</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>)</mo><mo> </mo><mn>25</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><mi>a</mi><mi>b</mi><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>5</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><mn>5</mn><mi>a</mi><mo>.</mo><mn>2</mn><mi>b</mi><mo>+</mo><msup><mfenced><mrow><mn>2</mn><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>5</mn><mi>a</mi><mo>-</mo><mn>2</mn><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mspace linebreak="newline"/><mi>H</mi><mi>o</mi><mi>ặ</mi><mi>c</mi><mo>:</mo><mspace linebreak="newline"/><mn>25</mn><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>4</mn><msup><mi>b</mi><mn>2</mn></msup><mo>−</mo><mn>20</mn><mi>a</mi><mi>b</mi><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>2</mn><mi>b</mi></mrow></mfenced><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><mn>2</mn><mi>b</mi><mo>.</mo><mn>5</mn><mi>a</mi><mo>+</mo><msup><mfenced><mrow><mn>5</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup><mspace linebreak="newline"/><mo>=</mo><msup><mfenced><mrow><mn>2</mn><mi>b</mi><mo>-</mo><mn>5</mn><mi>a</mi></mrow></mfenced><mn>2</mn></msup></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>)</mo><mo> </mo><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><mi>x</mi><mo>.</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>=</mo><msup><mfenced><mrow><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mn>2</mn></msup><mspace linebreak="newline"/><mi>H</mi><mi>o</mi><mi>ặ</mi><mi>c</mi><mo>:</mo><mspace linebreak="newline"/><msup><mi>x</mi><mn>2</mn></msup><mo>−</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><msup><mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></mfenced><mn>2</mn></msup><mo>+</mo><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>.</mo><mi>x</mi><mo>.</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>=</mo><msup><mfenced><mrow><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup></math>