Question

Factorize the expression $x-8x{y}^3$.

Answer 1

Factorize the given expression:

The given expression is $x-8x{y}^3$.

$$\begin{gathered} x-8x{y}^3=x\left(1-8y^3\right) \\ =x\left[1^3-{\left(2y\right)}^3\right] \end{gathered}$$

Use identity, $a^3-b^3=(a-b)\left(a^2+ab+b^2\right)$ to expand.

Here, $a=1,b=2y$.

Substitute values in identity we have:

$$\begin{gathered} x\left[1^3-{\left(2y\right)}^3\right]=x\left(1-2y\right)\left[1^2+2y\left(1\right)+{\left(2y\right)}^2\right] \\ =x\left(1-2y\right)\left(1+2y+4y^2\right) \end{gathered}$$

Thus, the expression, $x-8y^3=x\left(1-2y\right)\left(1+2y+4y^2\right)$.