Use binomial theorem to expand (x+3)^4

how did I get the coefficient of 6 for the 3rd expanded term?

by multiplying 4*3, and then dividing that by 2.

the 4(current coefficient), the 3(x's current exponent), and the 2(3's exponent on the following term).

so in essence, the product of the current coefficient by the exponent of the first term divided by the exponent of the second term in the following term.

now, you can always find the nth factor in any binomial by

where "k" is the term, say you want the 51st term? then k = 50.

and "n" is the exponent of the binomial.

constant acceleration- a

constant velocity- c

no velocity or acceleration- b

explanation:

for body moving with a constant acceleration, the rate of change of displacement changes over time. this is proven by the increasing gradient of the curve (a) against time.

a body that is moving at constant velocity covers equal distances over equal periods of time, thus the straight line with a constant gradient c.

a stationary body   covers no displacement as time elapses. thus the flat line with   zero gradient.