Question

expand the following ​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

$\: \: \: \: \: \mapsto \sf{{ \left( \dfrac{3x}{4} + \dfrac{2y}{5} \right) }^{3} }$

• $\small \sf{By \: Using \: Identity } \: _{ \bf\gray{ \scriptsize(a+b)^{3} =a³+b³+3ab(a+b)}}$

${\: \: \: \: \: \mapsto \sf{ \left( \dfrac{3x}{4} \right) }^{3} + \left(\dfrac{2y}{5} \right) ^{3} + 3 \times\dfrac{3x}{4} \times\dfrac{2y}{5}\left( \dfrac{3x}{4} + \dfrac{2y}{5} \right) }$

${\: \: \: \: \: \mapsto \sf{ \dfrac{ {(3x)}^{3} }{ {4}^{3} } } + \dfrac{ {(2y)}^{3} }{ {5}^{3} } + 3 \times\dfrac{3x}{ \cancel4} \times\dfrac{ \cancel2y}{5}\left( \dfrac{15x + 8y}{20} \right) }$

${\: \: \: \: \: \mapsto \sf{ \dfrac{ 27 {x}^{3} }{ 64 } } + \dfrac{ 8 {y}^{3} }{ 125 } + \dfrac{9xy}{10} \left( \dfrac{15x + 8y}{20} \right) }$

${\: \: \: \: \: \mapsto \sf{ \dfrac{ 27 {x}^{3} }{ 64 } } + \dfrac{ 8 {y}^{3} }{ 125 } + \dfrac{135 {x}^{2} y + 72x {y}^{2} }{200} }$

${\: \: \: \: \: \mapsto \sf{ \dfrac{ 27 {x}^{3} }{ 64 } } + \dfrac{ 8 {y}^{3} }{ 125 } + \dfrac{135 {x}^{2} y}{200} + \dfrac{72x {y}^{2} }{200} }$

${\: \: \: \: \: \mapsto \sf{ \dfrac{ 27 {x}^{3} }{ 64 } } + \dfrac{ 8 {y}^{3} }{ 125 } + \dfrac{27 {x}^{2} y}{40} + \dfrac{9x {y}^{2} }{25} }$

$\green{\boxed{\therefore~~ \sf{{ \left( \dfrac{3x}{4} + \dfrac{2y}{5} \right) }^{3} }{= \blue{\bf{ \dfrac{ 27 {x}^{3} }{ 64 } } + \dfrac{ 8 {y}^{3} }{ 125 } + \dfrac{27 {x}^{2} y}{40} + \dfrac{9x {y}^{2} }{25} } }}}$

$\pink{\begin{gathered}\tiny\begin{gathered}\small{\small{\small{\small{\small{\small{\small{\small{\small{\small{\begin{gathered}\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\red{ \bigstar} \: \underline{\bf{\orange{More \: Useful \: Formula}}}\\ {\boxed{\begin{array}{cc}\dashrightarrow \sf(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab \\\\\dashrightarrow \sf(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab \\\\\dashrightarrow \sf(a + b)(a - b) = {a}^{2} - {b}^{2} \\\\\dashrightarrow \sf(a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b) \\\\ \dashrightarrow\sf(a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b) \\ \\\dashrightarrow\sf a ^{3} + {b}^{3} = (a + b)(a ^{2} + {b}^{2} - ab) \\\\\dashrightarrow \sf a ^{3} - {b}^{3} = (a - b)(a ^{2} + {b}^{2} + ab \\\\\dashrightarrow \sf{a²+b²=(a+b)²-2ab}\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}}}}}}}}}}\end{gathered}\end{gathered}}$

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