$\frac{8}{27} x^{3} + 1 + \frac{4}{3} x^{2} + 2 x$

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Solution

The given expression to be factorized is

This can be written in the form

Take common from the last two terms,. Then we get

This can be written in the following form

Recall the formula for the cube of the sum of two numbers

Using the above formula, we have

We cannot further factorize the expression.

So, the required factorization is of is.

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Question 180(i)

Simplify

${[{(\frac{1}{2})}^{2} - {(\frac{1}{4})}^{3}]}^{- 1} \times 2^{- 3}$

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