Question

Factorise 27a^3+1/64 b^3+ 27a^2/4b+9a/16b^2

Answer 1

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Answer 2

Given,

• $27a^3+1/64 b^3+ 27a^2/4b+9a/16b^2$ is given.

To find,

• We have to factorize the given expression.

Solution,

We can simply factorize the given expression by using the following identity:

           (a+b)³ = a³+b³+3a²b+3ab²   (*)

Comparing the RHS of (*) and the given expression, we get

                  a³+b³+3a²b+3ab²                                    (1)

               $27a^3+1/64 b^3+ 27a^2/4b+9a/16b^2$             (2)

                (3a)³ + (1/4b)³ + 3(3a)(3a)(1/4b) + 3(3a)(1/4b)(1/4b)

                where a = 3a and b = 1/4b

then , (3a+1/4b)³ are the factors of $27a^3+1/64 b^3+ 27a^2/4b+9a/16b^2$.

Hence, $27a^3+1/64 b^3+ 27a^2/4b+9a/16b^2$ can be factorized as (3a+1/4b)³.