# SOLUTION: factor 8x^3y^5+16y^3x^5-40x^4y^4

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Question 115468: factor
8x^3y^5+16y^3x^5-40x^4y^4

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Factor out the GCF

Sort the terms

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 2 respectively.

Now multiply the first coefficient 1 and the last coefficient 2 to get 2. Now what two numbers multiply to 2 and add to the middle coefficient -5? Let's list all of the factors of 2:

Factors of 2:
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 2
1*2
(-1)*(-2)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -5? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -5

First NumberSecond NumberSum
121+2=3
-1-2-1+(-2)=-3

None of these pairs of factors add to -5. So the inner expression cannot be factored

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