SOLUTION: Please help me solve these problems. Factor. Check by multiplying 4x^5 y^3+16x^3 y^2+32xy and 9x^2=72x and factor by grouping 21x^3-15x^2+28x-20. Thank you very much!

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# 1


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 8 respectively.

Now multiply the first coefficient 1 and the last coefficient 8 to get 8. Now what two numbers multiply to 8 and add to the middle coefficient 4? Let's list all of the factors of 8:



Factors of 8:
1,2,4,8

-1,-2,-4,-8 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 8
1*8
2*4
(-1)*(-8)
(-2)*(-4)

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	8	1+8=9
2	4	2+4=6
-1	-8	-1+(-8)=-9
-2	-4	-2+(-4)=-6

None of these pairs of factors add to 4. So the expression cannot be factored

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Answer:
So factors to

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# 2



Start with the given equation


Subtract 72x from both sides.


Factor out the GCF 9x



Now set each factor equal to zero:

or


or Now solve for x in each case


So our answers are

or

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# 3
Start with the given expression

Group like terms


Factor out the GCF out of the first group. Factor out the GCF out of the second group


Since we have the common term , we can combine like terms

So factors to