Question

Factorize 3(2x-y)³+9(2x-y)²​

Answer 1

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$\longrightarrow \sf3(2x-y{)}^{3} +9(2x-y{)}^{2} \\ \\\longrightarrow \sf 3(8 {x}^{3} - {y}^{3} -12 {x}^{2} y + 6x {y}^{2}) + 9( {4x}^{2} + {y}^{2} - 4xy) \\ \\\longrightarrow \sf 24 {x}^{3} - 3{y}^{3} -24 {x}^{2} y + 18x {y}^{2} +{36x}^{2} + 9 {y}^{2} - 36xy$

Answer 2

Question :-

Factorize 3(2x-y)³+9(2x-y)²

Solution :-

=> 3(2x-y)³+9(2x-y)²

Express In The Form of (2x-y)³ and ( a + b )²

=>

$3(8x {}^{3} - y {}^{3} - 6xy(2x - y) )+ 9(4x {}^{2} + {y}^{2} - 2xy)$

=>

$3(8 {x}^{3} - {y}^{3} - 12 {x}^{2} y + 6x {y}^{2} + 9(4 {x}^{2} + {y}^{2} - 2xy)$

=>

$24 {x}^{3} - 3 {y}^{3} - 36 {x}^{2} y + 18x {y}^{2} + 36 {x}^{2} + 9 {y}^{2} - 18xy$

=> Final Answer⤵

$24 {x}^{3} - 3 {y}^{3} - 36 {x}^{2} y + 18x {y}^{2} + 36 {x}^{2} + 9 {y}^{2} - 18xy$