7
a
\(x^2+6x+9\\ =x^2+2.3.x+3^2\\ =\left(x+3\right)^2\)
b
\(9x^2-6x+1\\ =\left(3x\right)^2-2.3x.1+1^2\\ =\left(3x-1\right)^2\)
c
\(x^2y^2+xy+\dfrac{1}{4}\\ =\left(xy\right)^2+2.\dfrac{1}{2}.xy+\left(\dfrac{1}{2}\right)^2\\ =\left(xy+\dfrac{1}{2}\right)^2\)
d
\(\left(x-y\right)^2+6\left(x-y\right)+9\\ =\left(x-y\right)^2+2.3\left(x-y\right)+3^2\\ =\left(x-y+3\right)^2\)
8
a
\(x^2+6x+9=\left(x+3\right)^2\)
b
\(4x^2-4x+1=\left(2x-1\right)^2\)
c
\(9x^2-12xy+4y^2=\left(3x-2y\right)^2\)
d
\(\left(x-\dfrac{y}{3}\right)\left(x+\dfrac{y}{3}\right)=x^2-\dfrac{y^2}{9}\)