9w-w^3 I need someone to explain how do I factor this problem
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 )
Can someone please explain this step by step
To factor the expression 9w - w^3, you can follow these steps:
Step 1: Find the common factor.
In this case, both terms have a factor of w. So, factor out w:
w(9 - w^2)
Step 2: Factor the remaining expression.
Since 9 - w^2 is a difference of squares, you can factor it using the following formula:
a^2 - b^2 = (a + b)(a - b)
Applying this formula, rewrite 9 - w^2 as (3)^2 - w^2:
w(3 + w)(3 - w)
Therefore, the factored form of 9w - w^3 is w(3 + w)(3 - w).