Question

Factorize $8x^3+36x^{2}y+54x{y}^2+27y^3$.

Answer 1

Factorize the polynomial:

$$\begin{gathered} 8x^3+36x^{2}y+54x{y}^2+27y^3 \\ ={\left(2x\right)}^3+{\left(3y\right)}^3+3\times {\left(2x\right)}^2\times \left(3y\right)+3\times 2x\times {\left(3y\right)}^2 \end{gathered}$$

use the identity $a^3+b^3+3a^{2}b+3a{b}^2={(a+b)}^3$

$8x^3+36x^{2}y+54x{y}^2+27y^3={(2x+3y)}^3$

Hence the factorized form of polynomial $8x^3+36x^{2}y+54x{y}^2+27y^3$ is $\left(2x+3y\right)\left(2x+3y\right)\left(2x+3y\right)$