13:
a: \(16x^2+24x+9=\left(4x+3\right)^2\)
b: \(\dfrac{x^2}{4}-3x+9=\left(\dfrac{1}{2}x-3\right)^2\)
c: \(\dfrac{25}{x^2}-\dfrac{10}{x}+1=\left(\dfrac{5}{x}-1\right)^2\)
d: \(4x^4y^8+\left(x^2y^4\right)^4+4=\left[\left(x^2y^2\right)^2+2\right]^2\)
e: \(\left(2x-y\right)^2+2\left(2x-y\right)+1=\left(2x-y+1\right)^2\)
f: \(\left(2x-4y\right)^2+4x-8y+1=\left(2x-4y+1\right)^2\)
12:
a: \(\left(2x-3\right)^2=4x^2-12x+9\)
b: \(\left(\dfrac{5}{2}-x\right)^2=\dfrac{25}{4}-5x+x^2\)
c: \(\left(2x+3y\right)^2=4x^2+12xy+9y^2\)
d: \(\left(3x+\dfrac{2}{3}yz\right)^2=9x^2+4xyz+\dfrac{4}{9}y^2z^2\)
e: \(\left(\dfrac{xy}{2}-\dfrac{x}{3}\right)\left(\dfrac{xy}{2}+\dfrac{x}{3}\right)=\dfrac{x^2y^2}{4}-\dfrac{x^2}{9}\)
f: \(\left(2x-y+z\right)^2=4x^2+y^2+z^2-4xy-2yz+4xz\)
