Question

Factorize the expression $1-27a^3$.

Answer 1

Factorizing the given expression:

The given expression is $1-27a^3$.

$1-27a^3={\left(1\right)}^3-{\left(3a\right)}^3$

Use identity $x^3-y^3=(x-y)\left(x^2+xy+y^2\right)$ to expand.

Here, $x=1,y=3a$.

$$\begin{gathered} 1^3-{\left(3a\right)}^3=\left(1-3a\right)\left[1^2+3a+{\left(3a\right)}^2\right] \\ =\left(1-3a\right)\left(1+3a+9a^2\right) \end{gathered}$$

Thus, the expression, $1-27a^3=\left(1-3a\right)\left(1+3a+9a^2\right)$.