Question

Simplify:
(x2 - 9y2)
(x3 - 27y3)​

Answer 1

Answer:

use identities..

a2-b2 and a3-b3

Answer 2

Given:

$x^{2} -9y^{2}$

$x^{3} -27y^{3}$

To find:

Simplification of the expressions.

Solution:

$x^{2} -9y^{2}$ is an expression having 2 variables $x$ and $y$. This expression is of the form $a^{2}-b^{2}$. The identity $a^{2}-b^{2}$ is given by:

$a^{2}-b^{2}=(a+b)(a-b)$

Here, $a^{2}=x^{2} ,b^{2}=9y^{2}$

$9$ is a perfect square of $3$.

Thus, $a=x,b=3y$

On rechecking,

$a*a=x*x=x^{2}$

$b*b=3y*3y=9y^{2}$

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

$x^{3} -27y^{3}$ is an expression having 2 variables $x$ and $y$. This expression is of the form $a^{3}-b^{3}$. This is an identity and it is given by:

$a^{3} -b^{3}=(a-b)(a^{2}+ab+b^{2} )$

Here, $a^{3} =x^{3},b^{3} =27y^{3}$

$27$ is a perfect cube of $3$.

Thus, $a=x,b=3y$

On rechecking,

$a*a*a=x*x*x=x^{3}$

$b*b*b=3y*3y*3y=27y^{3}$

Hence, $x^{3}-27y^{3}=(x-3y)(x^{2} +3xy+9y^{2} )$

The following simplifications of the expressions are obtained:

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

$x^{3}-27y^{3}=(x-3y)(x^{2} +3xy+9y^{2} )$