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Question 184928: 5x3y-125xy
2m3+16
2x3+6x2-3x-9
Answer by swiemers(10)   (Show Source):
You can put this solution on YOUR website! I'm assuming you are supposed to factor or simply the expressions, so that's how I'll solve them.
1. 5x^3y - 125xy
Factor out 5xy and get:
5xy(x^2 - 25)
Then you can factor the parentheses as the difference of two squares into:
5xy(x - 5)(x + 5)
2. 2m^3 + 16
Factor out a 2 and get:
2(x^3 + 8)
Then use the sum of two cubes rule to factor the parentheses into:
2(x + 2) (x^2 - 2x + 4)
3. 2x^3 + 6x^2 - 3x - 9
This one we need to factor by grouping. First, group the first two terms together:
2x^3 + 6x^2
We can factor out 2x^2 and get:
2x^2(x + 3)
Second, group the second two terms together:
-3x - 9
We can factor out a -3 and get:
-3(x + 3)
So all of our factored problem so far is:
2x^2(x + 3) -3(x + 3)
When you are factoring by grouping, you rewrite this as two parentheses. The first is what's inside the parentheses - as long as it is THE SAME. The second parentheses is what is left over. So, it would become:
(x + 3) (2x^2 - 3)
Hope this helps! Good luck! Sandy :-)
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