what will be the formula for
a ^ (4) + b ^ (4) in terms of (a+b)(something).
what will be the (something)?
2006-07-04 19:37:32 · 9 answers · asked by rajesh bhowmick 2 in Science & Mathematics ➔ Mathematics
there is no something, as a+b is not a factor of a^4+b^4.
a+b is factor of a^n+b^n only if n is odd.
2006-07-04 20:19:24 · answer #1 · answered by plzselectanotherone 2 · 1⤊ 0⤋
a^4 + b^4
= a^4 + 2 a^2 b^2 + b^4 - 2 a^2 b^2
= (a^2 + b^2)^2 - 2 a^2 b^2
= (a^2 + b^2)^2 - (sqrt(2) a b)^2
= (a^2 + sqrt(2) a b + b^2) (a^2 - sqrt(2) a b + b^2)
2006-07-05 20:29:49 · answer #2 · answered by ymail493 5 · 0⤊ 0⤋
a^4 + b^4
= (a + b)(a³ - a²b + ab² - b³ + 2/(a + b))
the something is
(a³ - a²b + ab² - b³ + 2/(a + b))
^_^
2006-07-05 06:51:00 · answer #3 · answered by kevin! 5 · 0⤊ 0⤋
Try (a^4+b^4)/(a+b) using long division.
A previous responder suggested "synthetic division".
I didn't get very far though.
you could try multiplying out the "synthetic division" answer above to see if you get back to a^4 + b^4.
My long division didn't seem like it was going to end anytime soon.
2006-07-05 03:15:47 · answer #4 · answered by Anonymous · 0⤊ 0⤋
the formula will be 4ab^(2)
2006-07-05 02:42:37 · answer #5 · answered by sonia m 1 · 0⤊ 0⤋
(a+b)^4+4(a+b)^2+(2ab)^2-2a^4b^4
2006-07-05 05:20:26 · answer #6 · answered by ? 2 · 0⤊ 0⤋
(a+b)^4 - 2ab((a+b)^2)
2006-07-05 03:01:40 · answer #7 · answered by Srikanth 2 · 0⤊ 0⤋
(a^2-b^2)^2-2a^2 b^2
2006-07-05 04:05:26 · answer #8 · answered by deep 2 · 0⤊ 0⤋
do the math
2006-07-05 03:09:50 · answer #9 · answered by Anonymous · 0⤊ 0⤋