Question

Factorize each of the following expressions:
$54x^{6}y+2x^3{y}^4$

Answer 1

Given: $54x^{6}y+2x^3{y}^4$

$\therefore 54x^{6}y+2x^3{y}^4$
$=2x^{3}y(27x^3+y^3)$
$=2x^{3}y\left[\right(3x{)}^3+\left(y{)}^3\right]$
$=2x^{3}y\left[\right(3x+y\left)\right((3x{)}^2-3x\times y+y^2)]$
$=2x^{3}y(3x+y)(9x^2-3xy+y^2)$

Hence,$54x^{6}y+2x^3{y}^4$=$2x^{3}y(3x+y)(9x^2-3xy+y^2)$