\(x^2-6x+9=\left(x-3\right)^2\)
\(25+10x+x^2=\left(5+x\right)^2\)
\(\frac{1}{4}a^2+2ab^2+4b^4=\left(\frac{1}{2}a+2b^2\right)^2\)
\(\frac{1}{9}-\frac{2}{3}y^4+y^8=\left(\frac{1}{3}-y^4\right)^2\)
\(\left(3x+2\right)^2-4=\left(3x+2-2\right)\left(3x+2+2\right)=3x\left(3x+4\right)\)
\(4x^2-25y^2=\left(2x-5y\right)\left(2x+5y\right)\)
\(4x^2-49=\left(2x-7\right)\left(2x+7\right)\)
\(8z^3+27=\left(2z+3\right)\left(4z^2-6z+9\right)\)
\(\frac{9}{25}x^4-\frac{1}{4}=\left(\frac{3}{5}x^2-\frac{1}{2}\right)\left(\frac{3}{5}x^2+\frac{1}{2}\right)\)
