SOLUTION: I have to factor completely. I don't even know what I have to do here. I don't think I can subtract these from one another. Therefore, am I supposed write it out? Please help me un

Algebra ->  Exponents -> SOLUTION: I have to factor completely. I don't even know what I have to do here. I don't think I can subtract these from one another. Therefore, am I supposed write it out? Please help me un      Log On


   

Question 456713: I have to factor completely. I don't even know what I have to do here. I don't think I can subtract these from one another. Therefore, am I supposed write it out? Please help me understand what to do!
5b^4c^7d^6- 7b^5c^3d^8
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
5b%5E4c%5E7d%5E6+-+7b%5E5c%5E3d%5E8
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There are 2 terms. Look for common factors. Both have b, c & d, so factor that out.
= bcd%2A%285b%5E3c%5E6d%5E5+-+7b%5E4c%5E2d%5E7%29
Both terms still have bcd, so do it again.
= b%5E2c%5E2d%5E2%2A%285b%5E2c%5E5d%5E4+-+7b%5E3cd%5E6%29
And again
= b%5E3c%5E3d%5E3%2A%285bc%5E4d%5E3+-+7b%5E2d%5E5%29
Now the 2nd term has no "c", so factor out bd
= b%5E4c%5E3d%5E4%2A%285c%5E4d%5E2+-+7bd%5E4%29
Only d is common to both now. Factor out d^2, save a step
= b%5E4c%5E3d%5E6%2A%285c%5E4+-+7bd%5E2%29
----------------------------- That's all.
Doing it like that is tedious and time consuming. Here's a different approach:
5b%5E4c%5E7d%5E6+-+7b%5E5c%5E3d%5E8
The highest exponent of b is 4. Of c is 3, and of d is 6.
--> b%5E4c%5E3d%5E6
Divide the 2 terms by that.
= b%5E4c%5E3d%5E6+%2A+%285c%5E4+-+7bd%5E2%29