t2 - 36 = (t - 6)(t + 6)
This pattern is often called the difference of squares.
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That doesn't factor neatly. Applying the quadratic formula, we find two real solutions: 3 plus or minus -1.75 times the square root of 3 t = -0.0310889132455352 t = 6.0310889132455352
That doesn't factor neatly. Applying the quadratic formula, we find two imaginary solutions: (1 plus or minus the square root of -191) divided by 24t = 0.0416666 repeating + 0.5758447900452189it = 0.0416666 repeating - 0.5758447900452189iwhere i is the square root of negative one.
The factors of 54 are 1, 2, 3, 6, 9, 18, 27, 54
There are four terms in the expression: 4wt, 2wh, 6it and 3ih.4wt and 2wh have 2w in common and 6it and 3ih have 3i in common.4wt + 2wh can be written as 2w(t + h) and 6it + 3ih can be written as 3i(t + h).So the whole algerbraic expression can be written as:2w(t + h) + 3i(t + h)Now consider that 2w(t + h) and 3i(t + h) are two new terms and both have (t + h) in common.Rewriting the expression we get:(2w + 3i)(t + h).So, the required factors are (2w + 3i) and (t + h).
t4-81 is a difference of 2 squares and can be written as (t2-9)(t2+9) t2+9 can't be further factorised but t2-9 is a difference of 2 squares again and can be factorised to (t+3)(t-3) so the factors of t4-81 are :(t2+9)(t+3)(t-3) Hope this helps :-) I believe the answer you are looking for is (t - 3)(t + 3)(t 2 + 9)