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Looking at we can see that the first term is and the last term is where the coefficients are 1 and 51 respectively.
Now multiply the first coefficient 1 and the last coefficient 51 to get 51. Now what two numbers multiply to 51 and add to the middle coefficient -20? Let's list all of the factors of 51:
Factors of 51:
1,3,17,51
-1,-3,-17,-51 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 51
1*51
3*17
(-1)*(-51)
(-3)*(-17)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to -20? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -20
First Number
Second Number
Sum
1
51
1+51=52
3
17
3+17=20
-1
-51
-1+(-51)=-52
-3
-17
-3+(-17)=-20
From this list we can see that -3 and -17 add up to -20 and multiply to 51
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 )
(