Question

Factorise: $21x^2{y}^3+27x^3{y}^3$

• A. $3x^2{y}^3(7+9x)$
• B. $3x^2{y}^2(7y+9x)$
• C. $7xy+9x^{2}y$
• D. $7\times 3\times 4(x+y)$

Answer 1

The correct option is A

$3x^2{y}^3(7+9x)$

Consider the given expression,

$21x^2{y}^3+27x^3{y}^3$

$21x^2{y}^3$ can be written as,
$21x^2{y}^3=3\times 7\times x\times x\times y\times y\times y$...(i)

$27x^3{y}^3$ can be written as,

$27x^3{y}^3=3\times 3\times 3\times x\times x\times x\times y\times y\times y$....(ii)

From (i) and (ii), taking the common factors, we get
$21x^2{y}^3+27x^3{y}^3$

$=3\times x\times x\times y\times y\times y(7+9x)$
$=3x^2{y}^3(7+9x)$

Therefore, the factors of $21x^2{y}^3+27x^3{y}^3$ are $3x^2{y}^3$ and $(7+9x)$.

i.e., $21x^2{y}^3+27x^3{y}^3=3x^2{y}^3(7+9x)$