SOLUTION: Factor.
a^2 + 16a + 64
Algebra.Com
Question 132424: Factor.
a^2 + 16a + 64
Found 2 solutions by jim_thompson5910, edjones:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Looking at we can see that the first term is and the last term is where the coefficients are 1 and 64 respectively.
Now multiply the first coefficient 1 and the last coefficient 64 to get 64. Now what two numbers multiply to 64 and add to the middle coefficient 16? Let's list all of the factors of 64:
Factors of 64:
1,2,4,8,16,32
-1,-2,-4,-8,-16,-32 ...List the negative factors as well. This will allow us to find all possible combinations
These factors pair up and multiply to 64
1*64
2*32
4*16
8*8
(-1)*(-64)
(-2)*(-32)
(-4)*(-16)
(-8)*(-8)
note: remember two negative numbers multiplied together make a positive number
Now which of these pairs add to 16? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 16
| First Number | Second Number | Sum | | 1 | 64 | 1+64=65 |
| 2 | 32 | 2+32=34 |
| 4 | 16 | 4+16=20 |
| 8 | 8 | 8+8=16 |
| -1 | -64 | -1+(-64)=-65 |
| -2 | -32 | -2+(-32)=-34 |
| -4 | -16 | -4+(-16)=-20 |
| -8 | -8 | -8+(-8)=-16 |
From this list we can see that 8 and 8 add up to 16 and multiply to 64
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
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Answer:
So factors to
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
(a+8)^2
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