Question

Factorise: $18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$

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

Answer 1

The correct option is A

$9x^2{y}^2(2xy-3y+4x)$

Consider the given expression,

$18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$...(i)

$18x^3{y}^3$ can be written as,
$18x^3{y}^3=2\times 3\times 3\times x\times x\times x\times y\times y\times y$...(ii)

$27x^2{y}^3$ can be written as,
$27x^2{y}^3=3\times 3\times 3\times x\times x\times y\times y\times y$...(iii)

$36x^3{y}^2$ can be written as,
$36x^3{y}^2=2\times 2\times 3\times 3\times x\times x\times x\times y\times y$...(iv)
From (ii),(iii) and (iv), the common factors are $3^2$, $x^2$ and $y^2$.

Taking the common factors $3^2$, $x^2$ and $y^2$ from (i), we get
$18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$
$=9x^2{y}^2(2xy-3y+4x)$

$\Rightarrow 18x^3{y}^3-27x^2{y}^3+36x^3{y}^2=9x^2{y}^2(2xy-3y+4x)$

Therefore, the factors of $18x^3{y}^3-27x^2{y}^3+36x^3{y}^2$ are $9x^2{y}^2$ and $2xy-3y+4x$.