Question

Expand the following using either the Binomial Theorem or Pascal’s Triangle. (x - 5)5

Answer 1

Pakal triangle is hard to do with long things, but it is easy up to like 5 degree
we look at the row for 5th degree (6th row)
the sequence is
1,5,10,10,5,1
that is the coeficients

for (a+b)^5 that is
1a^5b^0+5a^4b^1+10a^3b^2+10a^2b^3+5a^1b^4+1a^0b^5
see the exponents each time add to 5

so
1x^5(-5)^0+5x^4(-5)^1+10x^3(-5)^2+10x^2(-5)^3+5x^1(-5)^4+1x^0(-5)^5=
x^5-25x^4+250x^3-1250