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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 10 respectively.
Now multiply the first coefficient 1 and the last coefficient 10 to get 10. Now what two numbers multiply to 10 and add to the middle coefficient 7? Let's list all of the factors of 10:
Factors of 10:
1,2,5,10
-1,-2,-5,-10 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 10
1*10
2*5
(-1)*(-10)
(-2)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 7
First Number
Second Number
Sum
1
10
1+10=11
2
5
2+5=7
-1
-10
-1+(-10)=-11
-2
-5
-2+(-5)=-7
From this list we can see that 2 and 5 add up to 7 and multiply to 10
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 )
(