Expanding problem? Its algebra 2 please help me?

Question

what is the 2nd term of (2x^4-i)^7 when you expand and i also need help with this one. 3rd term of (x/2+4y)^5 . i appreciate it if you help me out

Answer 1

You can expand any equation using
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
etc. Note that the coefficient of the second term is always the power: (a+b)^2 = 1a^2 + 2ab + 1b^2
so the second term of (2x^4-i)^7 is
7*(2x^4)^6*(-i)
or
-7*2^6*i*x^24

The third term of (x/2+4y)^5 uses the (1 5 10 10 5 1) line:
10*(x/2)^3*(4y)^2
= 10/8*16*x^3*y^2
= 20x^3y^2