Question

$\: Factorize : \: 8 {a}^{3} + 27$​

Answer 1

$\bf \: Factorize : \: 8 {a}^{3} + 27$

$: \implies \sf \: {(2a)}^{3} + {(3)}^{3}$

$: \implies \sf \: (2a + 3) \bigg( {(2a)}^{2} - (2a)(3) + {(3)}^{2} \bigg)$

$\boxed{ \pink{ \because \: \bf \: {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}}$

$: \implies \bf \: (2a + 3)( {4a}^{2} - 6a + 9)$

More Information:-

• $\purple{ \sf \:(a + b)^{2} = {a}^{2} + {b}^{2} + 2ab }$
• $\purple{ \sf \:(a - b)^{2} = {a}^{2} + {b}^{2} - 2ab }$
• $\purple{ \sf \:(a + b)(a - b) = {a}^{2} - {b}^{2} }$
• $\purple{ \sf \: (a + b + c)^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab + 2bc + 2ca}$
• $\purple{ \sf \: (a + b) ^{3} = {a}^{3} + b^{3} + 3ab(a + b)}$
• $\purple{ \sf \: (a - b) ^{3} = {a}^{3} - b^{3} - 3ab(a - b)}$
• $\purple{ \sf \: a ^{3} + {b}^{3} = (a + b)(a ^{2} + {b}^{2} - ab)}$
• $\purple{ \sf \: a ^{3} - {b}^{3} = (a - b)(a ^{2} + {b}^{2} + ab)}$

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Answer 2

Step-by-step explanation:

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