SOLUTION: please help me
10x^2+11xy-6y^2
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Question 185536: please help me
10x^2+11xy-6y^2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
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Looking at we can see that the first term is and the last term is where the coefficients are 10 and -6 respectively.
Now multiply the first coefficient 10 and the last coefficient -6 to get -60. Now what two numbers multiply to -60 and add to the middle coefficient 11? Let's list all of the factors of -60:
Factors of -60:
1,2,3,4,5,6,10,12,15,20,30,60
-1,-2,-3,-4,-5,-6,-10,-12,-15,-20,-30,-60 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -60
(1)*(-60)
(2)*(-30)
(3)*(-20)
(4)*(-15)
(5)*(-12)
(6)*(-10)
(-1)*(60)
(-2)*(30)
(-3)*(20)
(-4)*(15)
(-5)*(12)
(-6)*(10)
note: remember, the product of a negative and a positive number is a negative number
Now which of these pairs add to 11? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 11
| First Number | Second Number | Sum | | 1 | -60 | 1+(-60)=-59 |
| 2 | -30 | 2+(-30)=-28 |
| 3 | -20 | 3+(-20)=-17 |
| 4 | -15 | 4+(-15)=-11 |
| 5 | -12 | 5+(-12)=-7 |
| 6 | -10 | 6+(-10)=-4 |
| -1 | 60 | -1+60=59 |
| -2 | 30 | -2+30=28 |
| -3 | 20 | -3+20=17 |
| -4 | 15 | -4+15=11 |
| -5 | 12 | -5+12=7 |
| -6 | 10 | -6+10=4 |
From this list we can see that -4 and 15 add up to 11 and multiply to -60
Now looking at the expression , replace with (notice adds up to . So it is equivalent to )
Now let's factor by grouping:
Group like terms
Factor out the GCF of out of the first group. Factor out the GCF of out of the second group
Since we have a common term of , we can combine like terms
So factors to
So this also means that factors to (since is equivalent to )
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Answer:
So factors to
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