Factorise: 27a^3 + 1/64a^3 + 27a^2/4b + 9a/16b^2
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assuming that the second term is 1/64b^3(hope this must be there in the question)
look as we see here that there are a^3+ b^3
so we will try it to compare with the identity of (a+b)^3 = a^3+b^3+3a^2b+3ab^2
on comparing 27a^3 with a^3
we get a= 3a and similarly on comparing 1/64b^3 with b^3 we get b= 1/4b
now we will cube (3a+1/4b)
= 27a^3+1/64b^3 + 3(9a^2)(1/4b) +3(3a)(1/16b^2)
= 27a^3+1/64b^3+27/4a^2b+9a/16b^2
by the above formula
now we get that (3a+1/4b)^3 are the factors of the above eq.
hope this might help you
look as we see here that there are a^3+ b^3
so we will try it to compare with the identity of (a+b)^3 = a^3+b^3+3a^2b+3ab^2
on comparing 27a^3 with a^3
we get a= 3a and similarly on comparing 1/64b^3 with b^3 we get b= 1/4b
now we will cube (3a+1/4b)
= 27a^3+1/64b^3 + 3(9a^2)(1/4b) +3(3a)(1/16b^2)
= 27a^3+1/64b^3+27/4a^2b+9a/16b^2
by the above formula
now we get that (3a+1/4b)^3 are the factors of the above eq.
hope this might help you
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