Question

$\huge\mathfrak{ϙᴜᴇsᴛɪᴏɴ }$
$\implies \sf expansion \: of \: {(3x - 2y)}^{3} is$
Options :-
$\rm \: (a)27 {x}^{3} - 8 {y}^{3} - 54 {x}^{2} y + 36x {y}^{2}$
$\rm \: (b)9 {x}^{2} + 8 {y}^{3} - 54 {x}^{2} y - 36x {y}^{2}$
$\rm \: (c)9 {x}^{2} - 8 {y}^{3} + 54 {x}^{2} y + 36x {y}^{2}$
$\rm \: (d)none \: of \: these$

Explain this clearly please!!
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Answer 1

$\sf \red{CORRECT \: ANSWER}$

$\sf(a)27 {x}^{3} - 8 {y}^{3} - 54 {x}^{2} y + 36x {y}^{2}$

$\sf \red{SOLUTION}$

$\sf{Using(a-b)³= {a}^{3} - {b}^{3} - 3 {a}^{2} b + 3 {ab}^{2} }$

$\sf{(3x -2 {y}^{} {)}^{3} = 27 {x}^{3} - 8 {y}^{3} - 54 {x}^{2} y + 36 {xy}^{2} }$

#CarryOnLearning

Answer 2

☆Answer

$\red{{(3x - 2y)}^{3} }\\ \color{lime}= 3(3x)( - 2y)(3x - 2y) \\ \green{ = {27x}^{3} - 8y {}^{3} - 18xy(3x - 2y) }\\ \color{green}= {27x}^{3} - 8y {}^{3} - 54 {x}^{2} y + 36 {xy}^{2}$

Hence, Option (a) is correct.