Question 334833
"I don't understand why this is the answer to this problem. 
t^4 - 1
(t^2 + 1) (t + 1) (t - 1)"


distributive property: a * (b + c) = ab + ac


example: 2 * (3 + 4) = 2 * 3 + 2 * 4 = 6 + 8 = 14


FOIL or First-Outer-Inner-Last is also distributive:


example: (ax + b)(cx + d) = ax * cx + ax * d + b * cx + b * d
(ax + b)(cx + d) = acx^2 + (ad + bc) * x + bd


associative property: this is just grouping, a + (b + c) = (a + b) + c 
or a(bc) = (ab)c or 2(3*4) = (2*3)4


commutative property: this means you can switch the numbers you multiplying or adding around, a + b = b + a or ab = ba or 2*3 = 3*2


now back to the problem


t^4 - 1 (we want to factor this)


(t^2 + 1)(t^2 - 1)
test by FOIL: t^4 - t^2 + t^2 - 1 = t^4 - 1 (notice outer and inner terms cancel out)


t^2 - 1 can also be factored by same method
(t + 1)(t - 1)


t^2 + 1 can not be easily factored, well not unless you want to go into complex numbers (complex number is number of form a+bi where a and b are real numbers and i is the square root of -1)


if you do want to go into complex numbers:


t^2 + 1 = (t + i)(t - i) = t^2 - i^2 = t^2 - -1 = t^2 + 1


so without going into that:


t^4 - 1 = (t^2 + 1)(t + 1)(t - 1)


I hope this helps