Question

factorise 9-a⁶+2a³b³-b⁶.​

Answer 1

I hope this will be helpful .

Answer 2

SOLUTION

TO FACTORISE

$\sf{9 - {a}^{6} + 2 {a}^{3} {b}^{3} - {b}^{6} }$

FORMULA TO BE IMPLEMENTED

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

EVALUATION

$\sf{9 - {a}^{6} + 2 {a}^{3} {b}^{3} - {b}^{6} }$

$\sf{ = 9 - ( {a}^{6} - 2 {a}^{3} {b}^{3} + {b}^{6}) }$

$\sf{ = 9 - \bigg[ { ({a}^{3} )}^{2} - 2. {a}^{3} . {b}^{3} + { ({b}^{3} )}^{2} \bigg] }$

$\sf{ = {(3)}^{2} - \bigg[ { ({a}^{3} - {b}^{3} )}^{2} \bigg] }$

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

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