9w-w^3 I need someone to explain how do I factor this problem

Answer 1

9 w - w ^ 3 = w ( 9 - w ^ 2 )

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Remark:

a ^ 2 - b ^ 2 = ( a - b ) ( a + b )

So:

9 - w ^ 2 = 3 ^ 2 - w ^ 2 = ( 3 - w ) ( 3 + w ) = ( 3 - w ) ( w + 3 )

( 3 - w ) = - ( w - 3 )

( 3 - w ) ( w + 3 ) = - ( w - 3 ) ( w + 3 )
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9 w - w ^ 3 = w ( 9 - w ^ 2 )= w ( 3 - w ) ( w + 3 ) =

= w * [ - ( w - 3 ) ] ( w + 3 ) =

- w * ( w - 3 ) ( w + 3 )

9 w - w ^ 3 = - w * ( w - 3 ) ( w + 3 )

Answer 2

Can someone please explain this step by step