Math, asked by nandini1541, 9 months ago

factorise 3√3x^3-5√5y^3

(please give the answer fastly)

Answers

Answered by Mihir1001

$\huge{\underline{\mathfrak{\textcolor{blue}{Answer :}}}}$

$\huge\boxed{( \sqrt{3} x - \sqrt{5} y)( 3 {x}^{2} + 2 \sqrt{15} xy + 5 {y}^{2} )}$

$\huge{\underline{\mathrm{\textcolor{red}{Step-by-step \: \: explanation :}}}}$

$\LARGE{\underline{\mathtt{\textcolor{violet}{Given :-}}}}$

$3 \sqrt{3} {x}^{3} - 5 \sqrt{5} {y}^{3}$

$\LARGE{\underline{\mathtt{\textcolor{green}{To \: \: find :-}}}}$

Factors of the given expression

$\LARGE{\underline{\mathtt{\textcolor{teal}{Concept \: \: used :-}}}}$

Factorisation

$\LARGE{\underline{\mathtt{\textcolor{blue}{Solution :-}}}}$

We have,

$\mapsto 3 \sqrt{3} {x}^{3} - 5 \sqrt{5} {y}^{3}$

$= ( \sqrt{3} )( \sqrt{3} )( \sqrt{3} ) {x}^{3} - ( \sqrt{5} )( \sqrt{5} )( \sqrt{5} ) {y}^{3}$

$= {( \sqrt{3} )}^{3} {x}^{3} - {( \sqrt{5} )}^{3} {y}^{3}$

$= {( \sqrt{3} x)}^{3} - {( \sqrt{5} y)}^{3}$

$= ( \sqrt{3} x - \sqrt{5} y) \left( {( \sqrt{3} x)}^{2} + 2( \sqrt{3} x)( \sqrt{5} y) + {( \sqrt{5} y)}^{2} \right)$ ————— $\left[ \because {a}^{3} - {b}^{3} = ( a - b )( {a}^{2} + 2ab + {b}^{2} ) \right]$

$= ( \sqrt{3} x - \sqrt{5} y)( 3 {x}^{2} + 2 \sqrt{15} xy + 5 {y}^{2} )$

$\LARGE{\underline{\mathtt{\textcolor{magenta}{Conclusion :-}}}}$

$\large\boxed{3 \sqrt{3} {x}^{3} - 5 \sqrt{5} {y}^{3} = ( \sqrt{3} x - \sqrt{5} y)( 3 {x}^{2} + 2 \sqrt{15} xy + 5 {y}^{2} )}$

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factorise 3√3x^3-5√5y^3

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