c: \(25-a^2+2ab-b^2\)
\(=25-\left(a^2-2ab+b^2\right)\)
\(=5^2-\left(a-b\right)^2\)
\(=\left(5-a+b\right)\left(5+a-b\right)\)
d: \(\dfrac{1}{27}a^3y-8b^3y\)
\(=y\left(\dfrac{1}{27}a^3-8b^3\right)\)
\(=y\left[\left(\dfrac{1}{3}a\right)^3-\left(2b\right)^3\right]\)
\(=y\left(\dfrac{1}{3}a-2b\right)\left[\left(\dfrac{1}{3}a\right)^2+\dfrac{1}{3}a\cdot2b+\left(2b\right)^2\right]\)
\(=y\left(\dfrac{1}{3}a-2b\right)\left(\dfrac{1}{9}a^2+\dfrac{2}{3}ab+4b^2\right)\)
e: \(a^3-a+b^3-b\)
\(=\left(a^3+b^3\right)-\left(a+b\right)\)
\(=\left(a+b\right)\left(a^2-ab+b^2\right)-\left(a+b\right)\)
\(=\left(a+b\right)\left(a^2-ab+b^2-1\right)\)
g: \(5x^4y^2+20x^3y^2+20x^2y^2\)
\(=5x^2y^2\cdot x^2+5x^2y^2\cdot4x+5x^2y^2\cdot4\)
\(=5x^2y^2\left(x^2+4x+4\right)=5x^2y^2\left(x+2\right)^2\)
