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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 1 respectively.
Now multiply the first coefficient 1 and the last coefficient 1 to get 1. Now what two numbers multiply to 1 and add to the middle coefficient 2? Let's list all of the factors of 1:
Factors of 1:
1
-1 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 1
1*1
(-1)*(-1)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2
First Number
Second Number
Sum
1
1
1+1=2
-1
-1
-1+(-1)=-2
From this list we can see that 1 and 1 add up to 2 and multiply to 1
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 )
note: is equivalent to since the term occurs twice. So also factors to
(