SOLUTION: I need help solving this problem really bad factor: b^2+8ab-20c^2

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Question 540613: I need help solving this problem really bad factor: b^2+8ab-20c^2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression b%5E2%2B8ab-20c%5E2, we can see that the first coefficient is 1, the second coefficient is 8, and the last coefficient is -20.


Now multiply the first coefficient 1 by the last coefficient -20 to get %281%29%28-20%29=-20.


Now the question is: what two whole numbers multiply to -20 (the previous product) and add to the second coefficient 8?


To find these two numbers, we need to list all of the factors of -20 (the previous product).


Factors of -20:
1,2,4,5,10,20
-1,-2,-4,-5,-10,-20


Note: list the negative of each factor. This will allow us to find all possible combinations.


These factors pair up and multiply to -20.
1*(-20) = -20
2*(-10) = -20
4*(-5) = -20
(-1)*(20) = -20
(-2)*(10) = -20
(-4)*(5) = -20

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 8:


First NumberSecond NumberSum
1-201+(-20)=-19
2-102+(-10)=-8
4-54+(-5)=-1
-120-1+20=19
-210-2+10=8
-45-4+5=1



From the table, we can see that the two numbers -2 and 10 add to 8 (the middle coefficient).


So the two numbers -2 and 10 both multiply to -20 and add to 8


Now replace the middle term 8ab with -2ab%2B10ab. Remember, -2 and 10 add to 8. So this shows us that -2ab%2B10ab=8ab.


b%5E2%2Bhighlight%28-2ab%2B10ab%29-20c%5E2 Replace the second term 8ab with -2ab%2B10ab.


%28b%5E2-2ab%29%2B%2810ab-20c%5E2%29 Group the terms into two pairs.


b%28b-2a%29%2B%2810ab-20c%5E2%29 Factor out the GCF b from the first group.


b%28b-2a%29%2B10%28ab-2c%5E2%29 Factor out 10 from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.


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Answer:


So b%5E2%2B8ab-20c%5E2 factors to %28b%2B10%29%28b-2a%29.


In other words, b%5E2%2B8ab-20c%5E2=%28b%2B10%29%28b-2a%29.


Note: you can check the answer by expanding %28b%2B10%29%28b-2a%29 to get b%5E2%2B8ab-20c%5E2 or by graphing the original expression and the answer (the two graphs should be identical).


If you need more help, email me at jim_thompson5910@hotmail.com

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Jim