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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 8 respectively.
Now multiply the first coefficient 1 and the last coefficient 8 to get 8. Now what two numbers multiply to 8 and add to the middle coefficient 9? Let's list all of the factors of 8:
Factors of 8:
1,2,4,8
-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 8
1*8
2*4
(-1)*(-8)
(-2)*(-4)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 9? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 9
First Number
Second Number
Sum
1
8
1+8=9
2
4
2+4=6
-1
-8
-1+(-8)=-9
-2
-4
-2+(-4)=-6
From this list we can see that 1 and 8 add up to 9 and multiply to 8
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 )
(