\(a,9a^2b+12ab^3-18ab\)
\(=3ab\left(3a+4b^2-6\right)\)
\(b,x^2+2xy-25+y^2\)
\(=\left(x^2+2xy+y^2\right)-25\)
\(=\left(x+y\right)^2-5^2\)
\(=\left(x+y-5\right)\left(x+y+5\right)\)
a. 9a2b + 12ab3 - 18ab
= 3ab(3a + 4b2 - 6)
b. x2 + 2xy - 25 + y2
= (x2 + 2xy + y2) - 25
= (x + y)2 - 52
= (x + y + 5)(x + y - 5)