Question

factorisation the sums
a^6 - b^6​

Answer 1

Answer:

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a⁶-b⁶

= (a³)²-(b³)²

= (a³+b³)(a³-b³)

= (a+b)(a²+b²-ab)(a-b )(a²+b²+ab)

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Answer 2

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

We know ,

a³ + b³ = ( a + b ) ( a² - ab + b² )        ___ {i}

a³ - b³ = ( a - b ) ( a² + ab + b² )         ___ {ii}

From  {i} and {ii} ,

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

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

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