Factorise the following: 27-125a3-135a+225a2
The polynomial expression 27-125a3-135a+225a2,
can be written as 33-5a3-3325a+335a2 ….[1]
which is in the form of the algebraic identity a-b3=a3-b3-3aba-b
=a3-b3-3a2b+3ab2 ….[2]
By comparing equations [1] and [2], we can say that,
27-125a3-135a+225a2=3-5a3
Hence, 27-125a3-135a+225a2=(3-5a)(3-5a)(3-5a)
Factorise each of the following:
(i) (ii)
(iii) (iv)
(v)