x² - 2x + 2 + 4y² + 4y

= x² - 2x + 1 + 4y² + 4y + 1

= (x - 1)² + (2y + 1)²

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

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

a, \(25x^2+5xy+\frac{1}{4}y^2=\left(5x\right)^2+2.5x.\frac{1}{2}y+\left(\frac{1}{2}y\right)^2\)

\(=\left(5x+\frac{1}{2}y\right)^2\)

b, \(9x^2+12x+4=\left(3x\right)^2+2.3x.2+2^2=\left(3x+2\right)^2\)

c, \(x^2-6x+5-y^2-4y=\left(x^2-6x+9\right)-\left(y^2+4y+4\right)\)

\(=\left(x-3\right)^2-\left(y+2\right)^2=\left(x-y-5\right)\left(x+y-1\right)\)

d, \(\left(2x-y\right)^2+4\left(x+y\right)^2-4\left(2x-y\right)\left(x+y\right)\)

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

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

Có cái cc

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

(2x-4y)²+2(2x-4y)+1

=(2x-4y)²+2(2x-4y)+1²

=(2x-4y+1)²

x^2 + 4y^2 -6x + 4y +10

=x²-6x+9+4y²+4y+1

=(x-3)²+(2y+1)²

x^2-4y^2-6x+4y+10

= x^2- 2.x.3 + 9 + 4y^2-2.2y+1

= ( x - 3)^2+ (2y-1) ^2

a/ \(=\left(9x^2+30x+25\right)+\left(x^2+10x+25\right)=\)

\(=\left(3x+5\right)^2+\left(x+5\right)^2\)

b/ \(=\left(16x^2+8x+1\right)+\left(y^2-4y+4\right)=\left(4x+1\right)^2+\left(y-2\right)^2\)

c/ 

a) \(2x^2+2b^2=x^2+b^2+x^2+b^2=x^2+2xb+b^2+x^2-2xb+b^2=\left(x+b\right)^2+\left(x-b\right)^2\)

a, Đề sai bạn ơi phải là cộng 16 chứ không phải cộng 4

b,B= (x-2y+1)^2

thế còn c với d

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. \(4x^2+y^2+12x+4y+13\)

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

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

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

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

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

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

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