`a)x^2-2x+2+4y^2+4y`

`=x^2-2x+1+4y^2+4y+1`

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

`b)4x^2+y^2+12x+4y+13`

`=4x^2+12x+9+y^2+4y+4`

`=(2x+3)^2+(y+2)^2`

`c)x^2+17+4y^2+8x+4y`

`=x^2+8x+16+4y^2+4y+1`

`=(x+4)^2+(2y+1)^2`

`d)4x^2-12xy+y^2-4y+13`

`=4x^2-12x+9+y^2-4y+4`

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

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

b) \(4x^2+y^2+12x+4y+13=\left(2x+3\right)^2+\left(y+2\right)^2\)

c) \(x^2+17+4y^2+8x+4y=\left(x+4\right)^2+\left(2y+1\right)^2\)

d) \(4x^2-12x+y^2-4y+13=\left(2x-3\right)^2+\left(y-2\right)^2\)

a: \(x^2-2x+2+4y^2+4y\)

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

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

b: \(4x^2+12x+y^2+4y+13\)

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

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

c: \(x^2+8x+4y^2+4y+17\)

\(=x^2+8x+16+4y^2+4y+1\)

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

d: \(4x^2-12x+y^2-4y+13\)

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

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

\(4y^2-20y+25\)

\(=\left(2y\right)^2-2.2y.5+5^2\)

\(=\left(2y-5\right)^2\)

2x y 2  +  x 2 y 4 + 1 = x y 2 2 + 2.x y 2 .1 + 1 2  = x y 2 + 1 2

a)
=(x-2)³
b)\(\left(2-x\right)^3\)
c)\(\left(x+\dfrac{1}{3}\right)^3\)
d)\(\left(\dfrac{x}{2}+y\right)^3\)
e)
\(=\left(x-1\right)^2\left(x-1-15\right)+25\left[3\left(x-1\right)-5\right]\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-3-5\right)\)
\(=\left(x-1\right)^2\left(x-16\right)+25\left(3x-8\right)\)
 

a: (2x-1)*(2x-1)*(y*y-x+1)*(y*y-x+1)*(y*y-x+1)

b: =(2*a*a+2*c*c-a)/2

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

  9x²+4y²+2(3x+2y+6xy)+1

= 9x²+4y²+1+6x+4y+12xy

=(3x)²+(2y)²+1²+2.3x.2y+2.2y.1+2.3x.1   (1)

Thay 3x=m,2y=n,1=p

=>(1)=m²+n²+p²+2mn+2np+2pm=(m+n+p)²

=> 9x²+4y²+2(3x+2y+6xy)+1=(3x+2y+1)²

`9x^2+4y^2-12xy+6x-4y+1`

`=(3x)^2-2.3x.2y+(2y)^2+2(3x-2y)+1`

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

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

9x²+4y²-12xy+6x-4y+1=(3x-2y+1)²

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

(2x-4y)²+2(2x-4y)+1

=(2x-4y)²+2(2x-4y)+1²

=(2x-4y+1)²