SOLUTION: evalute the equation (p^3-8y^3) if-: p-4y=2 & py=8

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Question 803196: evalute the equation (p^3-8y^3) if-:
p-4y=2 & py=8
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
I do not like that problem. I think there is a typo.
I will solve the problem as typed, and the problem that was probably meant.

AS TYPED:
The problem as presented requires a lot of tedious work to get to 2 different ugly answers:
If p-4y=2 & py=8,
y=8%2Fp & p-4%288%2Fp%29=2-->p%5E2-32=2p-->p%5E2-2p-32=0-->p=1+%2B-+sqrt%2833%29

That's ugly, but it gets worse:

p=1%2Bsqrt%2833%29-->1%2Bsqrt%2833%29-4y=2-->4y=-1%2Bsqrt%2833%29-->y=%28sqrt%2833%29-1%29%2F4
That gets us to system%28p%5E3=36sqrt%2833%29%2B100%2Cy%5E3=%2836sqrt%2833%29-100%29%2F64%29-->p%5E3-8y%5E3=31.5sqrt%2833%29%2B112.5=about293.45

The other solution,
p=1-sqrt%2833%29-->1-sqrt%2833%29-4y=2-->4y=-1-sqrt%2833%29-->y=-%28sqrt%2833%29%2B1%29%2F4
That gets us to system%28p%5E3=100-36sqrt%2833%29%2Cy%5E3=-%2836sqrt%2833%29%2B100%29%2F64%29-->p%5E3-8y%5E3=112.5-31.5sqrt%2833%29=about-68.45

THE PROBLEM AS IT SHOULD BE:
p-2y=4 & py=8 allows for some clever maneuvering.
Since p%5E3-8y%5E3=p%5E3-%282y%29%5E3 ,
we could use some of those special products that the textbook represents as
a%5E3-b%5E3=%28a-b%29%28a%5E2%2Bab%2Bb%5E2%29 ,
%28a+%2B-+b%29%5E2=a%5E2+%2B-+2ab%2Bb%5E2 and
%28a+%2B-+b%29%5E3=a%5E3+%2B-+3a%5E2b+%2B3ab%5E2+%2B-+b%5E3

One way:
p%5E3-8y%5E3=p%5E3-%282y%29%5E3
= %28p-2y%29%28p%5E2%2Bp%282y%29%2B%282y%29%5E2%29
= 4%28p%5E2%2Bp%282y%29%2B%282y%29%5E2%29
= 4%28p%5E2-2%2Ap%282y%29%2B%282y%29%5E2%2B3p%282y%29%29
= 4%28%28p-2y%29%5E2%2B3p%282y%29%29
= 4%284%5E2%2B3p%282y%29%29
= 4%284%5E2%2B6py%29%29
= 4%284%5E2%2B6%2A8%29%29=highlight%28256%29

Another way to calculate p%5E3-8y%5E3=p%5E3-%282y%29%5E3
%28p-2y%29%5E3=p%5E3-3%2Ap%5E2%282y%29%2B3%2Ap%2A%282y%29%5E2-%282y%29%5E3
4%5E3=p%5E3-3%2Ap%5E2%282y%29%2B3%2Ap%2A%282y%29%5E2-8y%5E3
64=p%5E3-8y%5E3-3%2Ap%5E2%282y%29%2B3%2Ap%2A%282y%29%5E2
64=p%5E3-8y%5E3-3%2Ap%282y%29%28p-2y%29
64=p%5E3-8y%5E3-6%28py%29%28p-2y%29
64=p%5E3-8y%5E3-6%2A8%2A4
64%2B6%2A8%2A4=p%5E3-8y%5E3
p%5E3-8y%5E3=highlight%28256%29