\(1.E=9x^2-12xy+4y^2=\left(3x\right)^2-2\cdot3x\cdot2y+\left(2y\right)^2=\left(3x-2y\right)^2\\ 2.F=x^2+10x+25=x^2+2\cdot x\cdot5+5^2=\left(x+5\right)^2\\ 3.G=\dfrac{1}{4}x^2+x+1=\left(\dfrac{1}{2}x\right)^2+2\cdot\dfrac{1}{2}x\cdot1+1^2=\left(\dfrac{1}{2}x+1\right)^2\\ 4.H=x^2-2xy+y^2+2x-2y+1=\left(x-y\right)^2+2\left(x-y\right)\cdot1+1^2=\left(x-y+1\right)^2\\ 5.I=x^2+4y^2-4xy-2x+4y+1=\left(x^2-4xy+4y^2\right)-2\left(x-2y\right)+1\\ =\left(x-2y\right)^2-2\cdot\left(x-2y\right)\cdot1+1^2=\left(x-2y-1\right)^2\\ 6.K=\left(x+y\right)^2-4\left(x^2-y^2\right)+4\left(x-y\right)^2=\left(x+y\right)^2-4\left(x-y\right)\left(x+y\right)+\left[2\left(x-y\right)\right]^2\\ =\left(x+y\right)^2-2\cdot\left(x+y\right)\cdot\left[2\left(x-y\right)\right]^2+\left[2\left(x-y\right)\right]^2\\ =\left[\left(x+y\right)-2\left(x-y\right)\right]^2=\left(x+y-2x+2y\right)^2\\ =\left(3y-x\right)^2\)
