factor the expressions a) 18a^3*b^2-27a^4 b) 25y^2-16 c) z^6-144 d)m^3-125

a) We notice that neither term is a perfect square nor a
perfect cube, but they have the common factor 9a^3.

We'll
factorize by 9a^3 and we'll
get:

18a^3*b^2-27a^4 = 9a^3*(2b^2 -
3a)

b) Because the terms are perfect
squares, we'll have in the given expression, a difference of squares which it could be
written according to the rule:

a^2 - b^2 =
(a-b)(a+b)

25y^2-16 = (5y)^2 -
(4)^2

(5y)^2 - (4)^2 = (5y - 4)(5y +
4) 

c) Because the terms are again perfect
squares, we'll have in the given expression, a difference of squares which it could be
written according to the rule:

a^2 - b^2 =
(a-b)(a+b)

 z^6-144 = (z^3)^2 -
(12)^2

(z^3)^2 - (12)^2 = (z^3 + 12)(z^3 -
12)

Because of the fact that 12 is not a
perfect cube, although z^3 is, the brackets cannot be factored further
more.

d) Because the terms are perfect cubes, we'll have in
the given expression, a difference of cubes which it could be written according to the
rule:

a^3 - b^3 = (a-b)(a^2 + a*b +
b^2)

a^3 = m^3 and b^3 =
(5)^3

m^3-125 = m^3 -
5^3

m^3 - 5^3 = (m-5)(m^2 + 5*m +
25)