Question

Giúp mình với

Viết các biểu thức sau dưới dạng tổng của 2 bình phương

1, x² - 2x  + 2 + 4y² + 4y

2) 4x² - 4x + y² + 2y + 2

3) 4x² + 4x + 4y² + 4y + 2

4) 4x² + y² + 12x + 4y + 13

Answer 1

1. \(x^2-2x+2+4y^2+4y\)

\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)

\(=\left(x-1\right)^2+\left(2y+1\right)^2\)

2. \(4x^2-4x+y^2+2y+2\)

\(=\left(4x^2-4x+1\right)+\left(y^2+2y+1\right)\)

\(=\left(2x-1\right)^2+\left(y+1\right)^2\)

3. \(4x^2+4x+4y^2+4y+2\)

\(=\left(4x^2+4x+1\right)+\left(4y^2+4y+1\right)\)

\(=\left(2x+1\right)^2+\left(2y+1\right)^2\)

4. \(4x^2+y^2+12x+4y+13\)

\(=\left(4x^2+12x+9\right)+\left(y^2+4y+4\right)\)

\(=\left(2x+3\right)^2+\left(y+2\right)^2\)

Answer 2

\(x^2-2x+2+4y^2+4y\)

\(=\left(x^2-2x+1\right)+\left(4y^2+4y+1\right)\)

\(=\left(x-1\right)^2+\left(2y+1\right)^2\)

\(4x^2-4x+y^2+2y+2\)

\(=\left(2x-1\right)^2+\left(y+1\right)^2\)