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Looking at we can see that the first term is and the last term is where the coefficients are 3 and 5 respectively.
Now multiply the first coefficient 3 and the last coefficient 5 to get 15. Now what two numbers multiply to 15 and add to the middle coefficient 8? Let's list all of the factors of 15:
Factors of 15:
1,3,5,15
-1,-3,-5,-15 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 15
1*15
3*5
(-1)*(-15)
(-3)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 8? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 8
First Number
Second Number
Sum
1
15
1+15=16
3
5
3+5=8
-1
-15
-1+(-15)=-16
-3
-5
-3+(-5)=-8
From this list we can see that 3 and 5 add up to 8 and multiply to 15
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 )
(