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+--- Thread: Need help with two Algebra 2 problems >_< (/showthread.php?tid=3642)
Need help with two Algebra 2 problems >_< - Will - 2008-09-22
Hi, I was having a lot of trouble with these two algebra 2 problems.
You have to FACTOR each polynomial.
First one is:
(p+q)^3 - (p-q)^3
[^3 = to the power of 3]
and the second one is:
(a+b)^6 - (a-b)^6
[^6 = to the power of 6 etc.]
PLEASE show it step by step! I really do appreciate it if you do help me.
Need help with two Algebra 2 problems >_< - Fiel - 2008-09-22
Will Wrote:Hi, I was having a lot of trouble with these two algebra 2 problems.
You have to FACTOR each polynomial.
First one is:
(p+q)^3 - (p-q)^3
[^3 = to the power of 3]
and the second one is:
(a+b)^6 - (a-b)^6
[^6 = to the power of 6 etc.]
PLEASE show it step by step! I really do appreciate it if you do help me.
Lemme try the second one.
(a + b) ^ 6 - (a - b) ^ 6
Let A = (a + b) ^ 3
Let B = (a - b) ^ 3
A^2 - B^2 = (A + B)(A - B)
Place A and B back in
((a+b)^3 + (a - b) ^ 3)((a+b)^3 - (a - b)^3)
Let A = (a + b)
Let B = (a - b)
(A^3 + B^3)(A^3 - B^3)
idk where to go from here, lol
Need help with two Algebra 2 problems >_< - GreenTea - 2008-09-22
Will Wrote:Hi, I was having a lot of trouble with these two algebra 2 problems.
You have to FACTOR each polynomial.
First one is:
(p+q)^3 - (p-q)^3
[^3 = to the power of 3]
p3 + 3p2q + 3pq2 + q3 - (p3 -3p2q -3pq2 q3)
6p2q + 6pq2
6pq(p+q)
man... haven't done algebra since fist year uni...
fark been long long time.
Need help with two Algebra 2 problems >_< - Will - 2008-09-22
Eh i got the first one..it factors down to 2q(3p^2 + 2q^2)
and Fiel I don't really know if that's right..at least I don't get it..do you think you can explain each step a little? :f6:
Need help with two Algebra 2 problems >_< - butterfλi - 2008-09-22
Fiel Wrote:Lemme try the second one.
(a + b) ^ 6 - (a - b) ^ 6
Let A = (a + b) ^ 3
Let B = (a - b) ^ 3
A^2 - B^2 = (A + B)(A - B)
Place A and B back in
((a+b)^3 + (a - b) ^ 3)((a+b)^3 - (a - b)^3)
Let A = (a + b)
Let B = (a - b)
(A^3 + B^3)(A^3 - B^3)
idk where to go from here, lol
from there, you use sums and differences of cubes.
(A^3 + B^3)(A^3 - B^3)
http://www.purplemath.com/modules/specfact2.htm
X^3+ Y^3 = (x + y)(X^2 - XY + Y^2)
X^3 -Y^3 = (X - Y)(X^2 + XY + Y^2)
Need help with two Algebra 2 problems >_< - Will - 2008-09-23
argh I dont get it
I looked in the back of the book and the answer is supposed to be 4ab(3a^2 + b^2)(a^2 + 3b^2) but I dont understand how they got it!
Need help with two Algebra 2 problems >_< - Russt - 2008-09-23
Okay... here's basically what you need to know.
Difference of squares: m^2 - n^2 = (m+n)(m-n)
Difference of cubes: m^3 - n^3 = (m-n)(m^2+mn+n^2)
Sum of cubes: m^3 + n^3 = (m+n)(m^2-mn+n^2)
Basically what butterfli said. m and n can be anything. In the case of the first one m = p+q and n = p-q.
Can you do the second one from here or you need help?
Need help with two Algebra 2 problems >_< - butterfλi - 2008-09-23
using the sums and differences of cubes on (A^3 + B^3)(A^3 - B^3), you get
= (a+b)(a-b)(a²-ab+b²)(a²+ab+b²)
remember that fiel said
Let A = (a + b)
Let B = (a - b)
so that mess actually looks like
[(a+b)+(a-b)] x [(a+b)-(a-b)] x [(a+b)²-(a+b)(a-b)+(a-b)²] x [(a+b)²+(a+b)(a-b)+(a-b)²]
simplify it from there since its just a bunch of plus' and minus'. also because its plus' and minus', a buttload of things should cancel out.
Need help with two Algebra 2 problems >_< - Blankout - 2008-09-23
Answers!
Need help with two Algebra 2 problems >_< - Russt - 2008-09-23
Looks chaotic :f6:
Don't worry TS... precalc next year is easy.
Need help with two Algebra 2 problems >_< - tzk221 - 2008-09-23
Eww Precalc. Calculus is easier than Alg and PreCalc.
Need help with two Algebra 2 problems >_< - 'Lexy - 2008-09-23
tzk221 Wrote:Eww Precalc. Calculus is easier than Alg and PreCalc.
Are you kidding me?
Boo, Calculus.
Integrals suck.
Need help with two Algebra 2 problems >_< - Russt - 2008-09-23
tzk221 Wrote:Eww Precalc. Calculus is easier than Alg and PreCalc.Excluding vectors and some trig identities, the whole year in Precalc is basically review. I slept in that class and got an A.