Question

Write the binomial expansion of (t-3)^5

Answer 1

Answer:

Step-by-step explanation:

(t-3)^5 is the same as (t + (-3))^5

First:  t starts at the highest power and goes down and (-3) starts at the lowest power and goes up

Second: from the Pascal triangles take the coefficients  1  5  10  10  5  1

$1*t^{5} (-3)^{0} + 5*t^{4} (-3)^{1} +10*t^{3} (-3)^{2} +10*t^{2} (-3)^{3} +5*t^{1} (-3)^{4} +1*t^{0} (-3)^{5}$

Anything to power 0 is equal to 1

Negative number to an odd power is negative, to a even power is positive

$t^{5} -15t^{4} +90t^{3} -270t^{2} +405t -243$