Question

Factorise $3x^{7}y-81x^4{y}^4$

• A. $3x^{4}y\left[\right(x-3xy\left)\right(x^2-9x^2{y}^2+3x^{2}y\left)\right]$
• B. $3x^{4}y\left[\right(x-3xy\left)\right(x^2-9x^2{y}^2-3x^{2}y\left)\right]$
• C. $3x^{4}y\left[\right(x-3xy\left)\right(x^2+9x^2{y}^2+3x^{2}y\left)\right]$
• D. $3x^{4}y\left[\right(x-3xy\left)\right(x^2+9x^2{y}^2+3xy\left)\right]$

Answer 1

The correct option is C $3x^{4}y\left[\right(x-3xy\left)\right(x^2+9x^2{y}^2+3x^{2}y\left)\right]$

$3x^{7}y-81x^4{y}^4$
$=3x^{4}y[x^3-(3xy{)}^3]$
We know that,
{$x^3-y^3=(x-y)(x^2+xy+y^2)$ }
$=3x^{4}y\left[\right(x-3xy\left)\right(x^2+9x^2{y}^2+3x^{2}y\left)\right]$