Question

9(x+y)^2-x^2
factorize​

Answer 1

Answer:

9(x+y)^2-x^2

=[ 3( x + y) ]^2 - x ^ 2

= [ 3( x + y) + x ] [ 3( x + y) - x ]

=[ 4x + 3 y ] [ 2x + 3y ]

Answer 2

$\huge \bf9 {(x + y)}^{2} - {x}^{2} \\ \\ \large \tt \to {[3(x + y)]}^{2} - {(x)}^{2}$

Here,

The expression has turned into form of $\rm {a}^{2} - {b}^{2}$, which can be solved by identity ::-

$\sf \green{{a}^{2} - {b}^{2}} = \pink{ (a+b)(a-b)}$

Then,

$\huge \bf{[3(x + y)]}^{2} - {(x)}^{2} \\ \\ \to \tt[3(x + y) - x][3(x + y) + x] \\ \to \tt[3x + 3y - x][3x + 3y + x] \\ \large \to \red{\tt [2x + 3y][4x + 3y]}$

Hence,

• On factorizing $\rm 9(x + y)^{2} - x^{2} ,$ $\red{\tt [2x + 3y][4x + 3y]}$ is obtained.