SOLUTION: please help me asap 9x^2-35xy-4y^2 2x^2-xy+10xy-5y^2 64m^3+125n^3 250x^6+16y^3 please help me with these math problems above

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: please help me asap 9x^2-35xy-4y^2 2x^2-xy+10xy-5y^2 64m^3+125n^3 250x^6+16y^3 please help me with these math problems above      Log On


   

Question 236686: please help me asap
9x^2-35xy-4y^2
2x^2-xy+10xy-5y^2
64m^3+125n^3
250x^6+16y^3
please help me with these math problems above
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll help you with the first two to get you going.

# 1

Looking at 9x%5E2-35xy-4y%5E2 we can see that the first term is 9x%5E2 and the last term is -4y%5E2 where the coefficients are 9 and -4 respectively.

Now multiply the first coefficient 9 and the last coefficient -4 to get -36. Now what two numbers multiply to -36 and add to the middle coefficient -35? Let's list all of the factors of -36:



Factors of -36:
1,2,3,4,6,9,12,18

-1,-2,-3,-4,-6,-9,-12,-18 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -36
(1)*(-36)
(2)*(-18)
(3)*(-12)
(4)*(-9)
(-1)*(36)
(-2)*(18)
(-3)*(12)
(-4)*(9)

note: remember, the product of a negative and a positive number is a negative number


Now which of these pairs add to -35? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -35

First NumberSecond NumberSum
1-361+(-36)=-35
2-182+(-18)=-16
3-123+(-12)=-9
4-94+(-9)=-5
-136-1+36=35
-218-2+18=16
-312-3+12=9
-49-4+9=5



From this list we can see that 1 and -36 add up to -35 and multiply to -36


Now looking at the expression 9x%5E2-35xy-4y%5E2, replace -35xy with 1xy%2B-36xy (notice 1xy%2B-36xy adds up to -35xy. So it is equivalent to -35xy)

9x%5E2%2Bhighlight%281xy%2B-36xy%29%2B-4y%5E2


Now let's factor 9x%5E2%2B1xy-36xy-4y%5E2 by grouping:


%289x%5E2%2B1xy%29%2B%28-36xy-4y%5E2%29 Group like terms


x%289x%2By%29-4y%289x%2By%29 Factor out the GCF of x out of the first group. Factor out the GCF of -4y out of the second group


%28x-4y%29%289x%2By%29 Since we have a common term of 9x%2By, we can combine like terms

So 9x%5E2%2B1xy-36xy-4y%5E2 factors to %28x-4y%29%289x%2By%29


So this also means that 9x%5E2-35xy-4y%5E2 factors to %28x-4y%29%289x%2By%29 (since 9x%5E2-35xy-4y%5E2 is equivalent to 9x%5E2%2B1xy-36xy-4y%5E2)



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Answer:
So 9x%5E2-35xy-4y%5E2 completely factors to %28x-4y%29%289x%2By%29

In other words, 9x%5E2-35xy-4y%5E2=%28x-4y%29%289x%2By%29




# 2


2x%5E2-xy%2B10xy-5y%5E2 Start with the given expression


%282x%5E2-xy%29%2B%2810xy-5y%5E2%29 Group like terms


x%282x-y%29%2B5y%282x-y%29 Factor out the GCF x out of the first group. Factor out the GCF 5y out of the second group


%28x%2B5y%29%282x-y%29 Since we have the common term 2x-y, we can combine like terms


So 2x%5E2-xy%2B10xy-5y%5E2 factors to %28x%2B5y%29%282x-y%29


In other words, 2x%5E2-xy%2B10xy-5y%5E2=%28x%2B5y%29%282x-y%29