2007-02-19 03:35:40 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
and 3 binomials
2007-02-19 03:38:26 · update #1
Write t^4 - 16 as the product of 2 binomials? Note that, it's 2 BINOMIALS.
Using the difference of squares formula, i.e a ^ 2 - b ^ 2 = (a - b) (a + b), we can first try to factor the expression:
t ^ 4 - 16 = (t ^ 2) ^ 2 - 4 ^ 2 = (t ^ 2 - 4)(t ^ 2 + 4) = (t ^ 2 - 2 ^ 2)(t ^ 2 + 4) = (t - 2)(t + 2)(t ^ 2 + 4)
Binomial is a polynimial with 2 terms, so we can start trying to group the expression after we have factorred it, so it can become a product of 2 binomials.
t ^ 4 - 16 = [(t - 2)(t + 2)](t ^ 2 + 4) = (t ^ 2 - 4)(t ^ 2 + 4)
t ^ 4 - 16 = (t - 2) [(t + 2)(t ^ 2 + 4)] = (t - 2)(t ^ 3 + 2 t ^ 2 + 4t + 8) (WONG)
t ^ 4 - 16 = [(t - 2)(t ^ 2 + 4)] (t + 2) = (t ^ 3 - 2 t ^ 2 + 4t - 8)(t + 2) (WONG)
So the answer is:
t ^ 4 - 16 = (t ^ 2 - 4)(t ^ 2 + 4)
:)
2007-02-19 04:04:39 · answer #1 · answered by ? Woc Viet ? 2 · 0⤊ 0⤋
(t^2 + 4)(t^2 - 4) = (t^2 + 4) (t + 2)(t - 2)
2007-02-19 11:39:03 · answer #2 · answered by richardwptljc 6 · 0⤊ 0⤋
(t ^ 2 - 4)(t ^ 2 + 4)
2007-02-19 12:31:15 · answer #3 · answered by KASTA 2 · 0⤊ 0⤋
(t^2 - 4)(t^2 + 4)
2007-02-19 11:39:39 · answer #4 · answered by gjmb1960 7 · 0⤊ 0⤋
=(t^2-4)*(t^+4) =(t-2)*(t+2)*(t^2+4)
2007-02-19 11:42:36 · answer #5 · answered by santmann2002 7 · 0⤊ 0⤋
Difference of squares.
2007-02-19 11:38:15 · answer #6 · answered by Anonymous · 0⤊ 0⤋