I also need you to check and make sure that I am using the FOIL method correctly for this problem.
#82). 9w-w^3
9w-w^3=w*(w^2-9) I have to factor out the GCF, which is “w”.
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)
9w-w^3=w (9-w^2) =w (3-w) (w+3) = w*[-(w-3)] (w+3) =-w*(w-3) (w+3)
9w-w^3=-w^3+9w=-(w+3)*w*(w-3) Now it has become a perfect
To verify if you have used the FOIL method correctly in your solution, let's go through the steps:
1. The original expression is 9w - w^3.
2. You correctly factored out the greatest common factor (GCF), which is "w". So, the expression becomes:
9w - w^3 = w * (w^2 - 9)
3. You then simplified the expression w^2 - 9 using the difference of squares formula:
w^2 - 9 = (w + 3) * (w - 3)
4. Next, you distributed the negative sign to (w - 3) in the expression 3 - w:
3 - w = -(w - 3)
5. At this point, you have (3 - w) * (w + 3) = -(w - 3) * (w + 3).
6. Finally, you combined the factors:
(3 - w) * (w + 3) = -w * (w - 3) * (w + 3)
Based on these steps, it appears that you have correctly applied the FOIL method. The expression can be simplified further to -w^3 + 9w = -(w + 3) * w * (w - 3). However, note that the last part of your question got cut off. If you need assistance with that, please provide the missing information, and I'll be happy to help.