SOLUTION: factor:4k^2-16kv+16v^2

Question 168972: factor:4k^2-16kv+16v^2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

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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 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

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So our expression goes from and factors further to

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Answer:

So factors to

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