How do I factor this, Please help me.9w-w^3
w (9-w^2)
second factor is difference of squares
in general a^2-b^2 = (a-b)(a+b)
so
w (3-w)(3+w)
or
-w (w-3)(w+3)
Sorry Damon, I thought I was overlooked..I appreciate the help Thank you!!!
You are welcome.
To factor the expression 9w - w^3, you can start by finding the greatest common factor (GCF) of the terms. In this case, w is common to both terms. So, we can factor out w from each term:
w(9 - w^2)
Now, you need to check if the expression inside the parentheses, (9 - w^2), can be factored further. It is a difference of squares because 9 is a perfect square (3^2) and w^2 is also a perfect square. The difference of squares formula is a^2 - b^2 = (a + b)(a - b).
Using this formula, we can rewrite (9 - w^2) as:
(3)^2 - (w)^2 = (3 + w)(3 - w)
Now, substitute this factorized form back into the original expression:
w(3 + w)(3 - w)
So, the fully factored form of 9w - w^3 is w(3 + w)(3 - w).