a) \(3x\left(2x-1\right)+5y\left(2x-1\right)=\left(2x-1\right)\left(3x+5y\right)\)
b) \(x^3-2x^2-9x+18=x^2\left(x-2\right)-9\left(x-2\right)=\left(x-2\right)\left(x^2-9\right)=\left(x-2\right)\left(x-3\right)\left(x+3\right)\)
c) \(x^2-25-2xy+y^2=\left(x^2-2xy+y^2\right)-25=\left(x-y\right)^2-25=\left(x-y-5\right)\left(x-y+5\right)\)
d) \(2x^3-\dfrac{1}{4}=2\left(x^3-\dfrac{1}{8}\right)=2\left(x-\dfrac{1}{2}\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)=\left(2x-1\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)
a: \(3x\left(2x-1\right)+5y\left(2x-1\right)=\left(2x-1\right)\left(3x+5y\right)\)
b: \(x^3-2x^2-9x+18\)
\(=x^2\left(x-2\right)-9\left(x-2\right)\)
\(=\left(x-2\right)\left(x-3\right)\left(x+3\right)\)
c: \(x^2-2xy+y^2-25\)
\(=\left(x-y\right)^2-25\)
\(=\left(x-y-5\right)\left(x-y+5\right)\)
d: \(2x^3-\dfrac{1}{4}=2\left(x-\dfrac{1}{2}\right)\left(x^2+\dfrac{1}{2}x+\dfrac{1}{4}\right)\)
