Question

(5a – 3b)3
expand the following ​

Answer 1

Answer:

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Answer 2

$(iv) \: \: \: \sf { (5 a - 3b) }^{3}$

$\small{ \sf{Using \: Identity : \boxed{(a-b)³=a³-b³-3ab(a-b)}}}$

${ \: \: \: \: \: : \: \: \sf\implies(5a-3b)³=(5a)³-(3b)³-3 \times 5a \times 3b(5a-3b)}$

${ \: \: \: \: \: : \: \: \sf\implies(5a-3b)³=125a³-27b³ - 45ab(5a-3b)}$

${ \: \: \: \: \: : \: \: \sf\implies(5a-3b)³=125a³-27b³ - 45ab \times 5a-45ab \times (-3b)}$

${ \: \: \: \: \: : \: \: \sf\implies(5a-3b)³=125a³-27b³ - 225 {a}^{2} b +135a {b}^{2} }$

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