Question

3a + 2b = 5c, find the value of 27a³ + 8b³ - 125c³ if abc= 0

Answer 1

Answer:

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Answer 2

Answer:

$\mathfrak{- 54 {a}^{2} b - 36a {b}^{2}}$

$\red{ \underline{question}}$

$\implies$ 3a + 2b = 5c, find the value of 27a³ + 8b³ - 125c³ if abc= 0

$\green{ \underline{solution}}$

$\ \\find \implies 27 {a}^{3} + 8 {b}^{3} - 125 {c}^{3} \\ \\ according \: to \: the \: qestion \\ \\ \implies \: 3a + 2b = 5c \\ \\ taking \: cube \: on \: both \: sides \\ \\ \implies {(3a + 2b )}^{3} = {(5c)}^{3} \\ using \: identity \: \: \\ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) \\ \\ hence \\ \\ \implies {(3a)}^{3} + {(2b)}^{3} + 3 \times 3a \times 2b(3a + 2b) = {(5c)}^{3} \\ \\ \implies \: 27 {a}^{3} + 8 {b}^{3} + 18ab(3a + 2b) = 125 {c}^{3} \\ \\ \implies \: 27 {a}^{3} + 8 {b}^{3} - 125 {c}^{3} = \red{- 18ab(3a + 2b)} \\ \\ or \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = - 54 {a}^{2} b - 36a {b}^{2} \\ \\ \\ hope \: it \: helps \: u$