Question

Factorize the following $1-64a^3-12a+48a^2$.

Answer 1

Factorize the given polynomial

$$\begin{gathered} 1-64a^3-12a+48a^2 \\ {\left(1\right)}^3-{\left(4a\right)}^3+3\times 1\times {\left(4a\right)}^2-3\times {\left(1\right)}^2\times 4a \end{gathered}$$

Use the identity ${(x-y)}^3=-x^3+y^3-3x^{2}y+3x{y}^2$

$1-64a^3-12a+48a^2={(1-4a)}^3$

Hence, the factorized form of the polynomial $1-64a^3-12a+48a^2$ is $(1-4a)(1-4a)(1-4a)$