Question

a3-3a^2b+3ab2-2b3 factories
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Answer 1

Question:-

• Factorise a³ -3a²b + 3ab² - 2b³

Solution:-

${a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - 2 {b}^{3}$

$= ({a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3} ) - {b}^{3}$

$= {(a - b)}^{3} - {b}^{3}$

$= (a - b - b)( {(a - b)}^{2} + b(a - b) + {b}^{2} )$

$= (a - 2b)( {a}^{2} + {b}^{2} -2ab + ab - {b}^{2} + {b}^{2} )$

$=(a - 2b)( {a}^{2} + {b}^{2} - ab)$

Answer:-

• $(a - 2b)( {a}^{2} + {b}^{2} - ab)$