Looking at we can see that the first term is and the last term is where the coefficients are 1 and 4 respectively.
Now multiply the first coefficient 1 and the last coefficient 4 to get 4. Now what two numbers multiply to 4 and add to the middle coefficient 4? Let's list all of the factors of 4:
Factors of 4:
1,2
-1,-2 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 4
1*4
2*2
(-1)*(-4)
(-2)*(-2)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4
First Number
Second Number
Sum
1
4
1+4=5
2
2
2+2=4
-1
-4
-1+(-4)=-5
-2
-2
-2+(-2)=-4
From this list we can see that 2 and 2 add up to 4 and multiply to 4
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
(