SOLUTION: What is 2y squared + 20y + 18

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Question 422731: What is 2y squared + 20y + 18
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you want to factor this.




2y%5E2%2B20y%2B18 Start with the given expression.


2%28y%5E2%2B10y%2B9%29 Factor out the GCF 2.


Now let's try to factor the inner expression y%5E2%2B10y%2B9


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Looking at the expression y%5E2%2B10y%2B9, we can see that the first coefficient is 1, the second coefficient is 10, and the last term is 9.


Now multiply the first coefficient 1 by the last term 9 to get %281%29%289%29=9.


Now the question is: what two whole numbers multiply to 9 (the previous product) and add to the second coefficient 10?


To find these two numbers, we need to list all of the factors of 9 (the previous product).


Factors of 9:
1,3,9
-1,-3,-9


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


These factors pair up and multiply to 9.
1*9 = 9
3*3 = 9
(-1)*(-9) = 9
(-3)*(-3) = 9

Now let's add up each pair of factors to see if one pair adds to the middle coefficient 10:


First NumberSecond NumberSum
191+9=10
333+3=6
-1-9-1+(-9)=-10
-3-3-3+(-3)=-6



From the table, we can see that the two numbers 1 and 9 add to 10 (the middle coefficient).


So the two numbers 1 and 9 both multiply to 9 and add to 10


Now replace the middle term 10y with y%2B9y. Remember, 1 and 9 add to 10. So this shows us that y%2B9y=10y.


y%5E2%2Bhighlight%28y%2B9y%29%2B9 Replace the second term 10y with y%2B9y.


%28y%5E2%2By%29%2B%289y%2B9%29 Group the terms into two pairs.


y%28y%2B1%29%2B%289y%2B9%29 Factor out the GCF y from the first group.


y%28y%2B1%29%2B9%28y%2B1%29 Factor out 9 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.


%28y%2B9%29%28y%2B1%29 Combine like terms. Or factor out the common term y%2B1


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So 2%28y%5E2%2B10y%2B9%29 then factors further to 2%28y%2B9%29%28y%2B1%29


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Answer:


So 2y%5E2%2B20y%2B18 completely factors to 2%28y%2B9%29%28y%2B1%29.


In other words, 2y%5E2%2B20y%2B18=2%28y%2B9%29%28y%2B1%29.


Note: you can check the answer by expanding 2%28y%2B9%29%28y%2B1%29 to get 2y%5E2%2B20y%2B18 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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim