so i dont know the difference between the binomial theorem and pascals triangle. why do they give such different solutions.
one example.
(2x-3)^4 can give two very different (and long) solutions
why?
They don't they are the same.
(2x-3)^4
The 4 line of pascals triangle is 14641
so
(2x−3)4=1∗(2x)4+4∗(2x)3∗(−3)1+6∗(2x)2∗(−3)2+4∗(2x)1∗(−3)3+1∗(−3)4=1∗16x4+4∗8x3∗−3+6∗4x2∗9+4∗2x1∗−27+1∗81 =1∗16x4+4∗−24x3+6∗36x2+4∗−54x+1∗81 =16x4−96x3+216x2−216x+81
There could be careless errors but this should be the same as if you expand it in any other way.