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Question

Factorise the following: 27-125a3-135a+225a2


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Solution

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)


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