Question

-9a^2 -12ab -4b^2 +81 factorise
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Answer 1

☆ Given Question :-

$\bf \:Factorize \:: - {9a}^{2} - 12ab - 4 {b}^{2} + 81$

$\huge \orange{AηsωeR} ✍$

$\begin{gathered}\begin{gathered}\bf{\underline{\underline{Given :-}}}\end{gathered}\end{gathered}$

$\bf \: - {9a}^{2} - 12ab - 4 {b}^{2} + 81$

$\begin{gathered}\begin{gathered}\bf{\underline{\underline{To Find :-}}}\end{gathered}\end{gathered}$

$\bf \:Factorize$

$\begin{gathered}\begin{gathered}\bf{\underline{\underline{Identity \: used :-}}}\end{gathered}\end{gathered}$

$\bf \:1. \: (a + b)² = a² + 2ab + b² \\ \bf \:</p><p>2. \: (a - b)² = a² - 2ab + b² \\ \bf \:3. \: </p><p>a² - b² = (a + b)(a - b)$

$\begin{gathered}\Large{\bold{\pink{\underline{CaLcUlAtIoN\::}}}} \end{gathered}$

$\bf \:  ⟼ - {9a}^{2} - 12ab - 4 {b}^{2} + 81$

$\bf \:  ⟼ 81 - {9a}^{2} - 12ab - 4 {b}^{2}$

$\bf \:  ⟼ 81 - ({9a}^{2} + 12ab + 4 {b}^{2} )$

$\bf \:  ⟼ 81 - ( {(3a)}^{2} + 2 \times 3a \times 2b + {(2b)}^{2} )$

$\bf \:  ⟼ 81 - {(3a + 2b)}^{2}$

$\bf \:  ⟼ {9}^{2} - {(3a + 2b)}^{2}$

$\bf \:  ⟼ (9 + 3a + 2b)(9 - 3a - 2b)$