Looking at we can see that the first term is and the last term is where the coefficients are 1 and 25 respectively.
Now multiply the first coefficient 1 and the last coefficient 25 to get 25. Now what two numbers multiply to 25 and add to the middle coefficient 10? Let's list all of the factors of 25:
Factors of 25:
1,5
-1,-5 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 25
1*25
5*5
(-1)*(-25)
(-5)*(-5)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 10
First Number
Second Number
Sum
1
25
1+25=26
5
5
5+5=10
-1
-25
-1+(-25)=-26
-5
-5
-5+(-5)=-10
From this list we can see that 5 and 5 add up to 10 and multiply to 25
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
(