Looking at we can see that the first term is and the last term is where the coefficients are 35 and -1 respectively.
Now multiply the first coefficient 35 and the last coefficient -1 to get -35. Now what two numbers multiply to -35 and add to the middle coefficient -2? Let's list all of the factors of -35:
Factors of -35:
1,5,7,35
-1,-5,-7,-35 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to -35
(1)*(-35)
(5)*(-7)
(-1)*(35)
(-5)*(7)
note: remember, the product of a negative and a positive number is a negative 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
-35
1+(-35)=-34
5
-7
5+(-7)=-2
-1
35
-1+35=34
-5
7
-5+7=2
From this list we can see that 5 and -7 add up to -2 and multiply to -35
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 )
(