Question

Factorise the equation 9(x+y)² - x²​

Answer 1

$\Large\purple{\textbf{\textsf{Answer:}}}$

$\bf{~~~~~~~~9(x+y)^{2}-x^{2}}$

$\bf{Identity~to~be~used:}$

$\bf{(a+b)^{2}=a^{2}+2ab+y^{2}}$

$\bf{: \longrightarrow 9(x^{2}+2xy+y^{2})-x^{2}}$

$\bf{: \longrightarrow 9x^{2}+18xy+9y^{2}-x^{2}}$

$\bf{: \longrightarrow 8x^{2}+18xy+9y^{2}}$

$\bf\color{navy}{Here,~~S=18~~P=72~~~(6~,~~12)}$

$\bf{: \longrightarrow (8x^{2}+12xy)+(6xy+9y^{2})}$

$\bf{: \longrightarrow [4x(2x+3y)~]+[3y(2x+3y)~]}$

$\bf{: \longrightarrow (2x+3y)(4x+3y)}$

$\sf{}$

$\bf\therefore{{\underline{The~factors~are}}:}$

$\bf{{\purple{2x+3y}}~~~and~~~{\purple{4x+3y}}}$

$\large\purple{\textbf{\textsf{Hope~it~helps..!!}}}$

Answer 2

Qᴜᴇsᴛɪᴏɴ:-

Factorise the equation 9(x+y)² - x²

Aɴsᴡᴇʀ:-

$\sf\begin{gathered}9 {(x + y)}^{2} - {x}^{2} \\ = (3 {(x + y))}^{2} - {(x)}^{2} \\ = (3x + 3y + x)(3x + 3y - x) \\ = (4x + 3y)(2x + 3y) \end{gathered}$