Question

Please Solve It :-




$(3m \: - \: 2n)(2m \: - \: 3n)$
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Answer 1

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

Solve it:-

• $(3m \: - \: 2n)(2m \: - \: 3n)$

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$\large\underline{ \underline{ \sf \maltese{ \: Solution:- }}}$

$\begin{gathered}\begin{gathered}\begin{gathered}: \implies \underline\blue{ \boxed{\displaystyle \sf \bold\orange{\: (3m \: - \: 2n)\: (2m \: - \: 3n) }} }\\ \\\end{gathered}\end{gathered}\end{gathered}$

$\underbrace\red{\boxed{ \sf \blue{ Multiplying \: the \: Terms }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 3m ( 2m - 3n ) - 2n (2m - 3n) }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{3m \: \times \: 2m \: - 3m \times 3nm - 2n \times 2m \: + \: 2n \times 3n</p><p> }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{6m}^{2} - \: 9mn \: - \: 4mn \: + \: {6n}^{2} { }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ {6m}^{2} - \: 13mn \: + \: {6n}^{2} }}$

$\underbrace\green{\boxed{ \sf \purple{ When \:m\: = \:1 \:and\: n\: = \:-1 , \:we \: get }}}$

$\qquad \quad {:} \longrightarrow \sf{\sf{{6m}^{2} \: - \: 13mn \: + {6n}^{2} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 6 \times {(1)}^{2} - 13 \times 1 \times ( - 1) \: + 6 \times {( - 1)}^{2} }}$

$\qquad \quad {:} \longrightarrow \sf{\sf{ 6 \: + \: 13 \: + \: 6 }}$

$\qquad\quad {:} \longrightarrow \underline \red{\boxed{\sf{25 }}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Solution \: of \: the \: Equation \: = \underline {\underline{ 25}}}\\\end{gathered}\end{gathered}$

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More For Knowledge:-

$\begin{gathered}\boxed{\begin{minipage}{5 cm}\bf{\dag}\:\:\underline{\text{Law of Exponents :}}\\\\\bigstar\:\:\sf\dfrac{a^m}{a^n} = a^{m - n}\\\\\bigstar\:\:\sf{(a^m)^n = a^{mn}}\\\\\bigstar\:\:\sf(a^m)(a^n) = a^{m + n}\\\\\bigstar\:\:\sf\dfrac{1}{a^n} = a^{-n}\\\\\bigstar\:\:\sf\sqrt[\sf n]{\sf a} = (a)^{\dfrac{1}{n}}\end{minipage}}\end{gathered}$

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