Calculate the binomial expansion of (2x+6)^5 up to x^3 where x is decreasing.

In order to use the binomial expansion, we must have an 'x' with no coefficients - so no number before it.
So we take out a factor of 2:(2(x+3))^5
We can then simplify to:32(x+3)^5
by expanding out 2^5.
Now we use the binomial theorem you can see on your formula sheet you have with you, in this case letting n=5, and a=3. We need this down to x^3. So we get:
32((5C0)x^5+(5C1)3x^4+(5C2)*(3^2)*x^3+...)
Don't forget the 32 on the outside because that does matter!
We only need it to x^3 so we can ignore anything after and then simplify this:
32(x^5+15x^4+90x^3)
And finally, we expand out to get...
32 x^5+480 x^4+2280 x^3