SOLUTION: factor each expression h to the second power+ 10h + 25

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Question 601670: factor each expression
h to the second power+ 10h + 25
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Looking at the expression h%5E2%2B10h%2B25, we can see that the first coefficient is 1, the second coefficient is 10, and the last term is 25.


Now multiply the first coefficient 1 by the last term 25 to get %281%29%2825%29=25.


Now the question is: what two whole numbers multiply to 25 (the previous product) and add to the second coefficient 10?


To find these two numbers, we need to list all of the factors of 25 (the previous product).


Factors of 25:
1,5,25
-1,-5,-25


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


These factors pair up and multiply to 25.
1*25 = 25
5*5 = 25
(-1)*(-25) = 25
(-5)*(-5) = 25

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


First NumberSecond NumberSum
1251+25=26
555+5=10
-1-25-1+(-25)=-26
-5-5-5+(-5)=-10



From the table, we can see that the two numbers 5 and 5 add to 10 (the middle coefficient).


So the two numbers 5 and 5 both multiply to 25 and add to 10


Now replace the middle term 10h with 5h%2B5h. Remember, 5 and 5 add to 10. So this shows us that 5h%2B5h=10h.


h%5E2%2Bhighlight%285h%2B5h%29%2B25 Replace the second term 10h with 5h%2B5h.


%28h%5E2%2B5h%29%2B%285h%2B25%29 Group the terms into two pairs.


h%28h%2B5%29%2B%285h%2B25%29 Factor out the GCF h from the first group.


h%28h%2B5%29%2B5%28h%2B5%29 Factor out 5 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.


%28h%2B5%29%28h%2B5%29 Combine like terms. Or factor out the common term h%2B5


%28h%2B5%29%5E2 Condense the terms.


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Answer:


So h%5E2%2B10h%2B25 factors to %28h%2B5%29%5E2.


In other words, h%5E2%2B10h%2B25=%28h%2B5%29%5E2.


Note: you can check the answer by expanding %28h%2B5%29%5E2 to get h%5E2%2B10h%2B25 or by graphing the original expression and the answer (the two graphs should be identical).

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