Just to be sure whats the binomial expansion of (2x+5)^4?

What did you come up with? We can check it for you.

In general, in the expansion of (a + b)^n, the terms are:
C(n,k) * a^(n-k) * b^k

a = 2x
b = 5

C(4,0) = 1
C(4,1) = 4
C(4,2) = 6
C(4,3) = 4
C(4,4) = 1

Terms:
1 * (2x)^4 * 5^0 = 16x^4
4 * (2x)^3 * 5^1 = 160x^3
6 * (2x)^2 * 5^2 = 600x^2
4 * (2x)^1 * 5^3 = 1000x
1 * (2x)^0 * 5^4 = 625

Answer:
16x^4 + 160x^3 + 600x^2 + 1000x + 625

(2x + 5)⁴

= ₄C₀(2x)⁴ + ₄C₁(2x)³(5) + ₄C₂(2x)²(5)² + ₄C₃(2x)(5)³ + ₄C₄(5)⁴

= (1)(16x⁴) + (4)(8x³)(5) + (6)(4x²)(25) + (4)(2x)(125) + (1)(625)

= 16x⁴ + 160x³ + 600x² + 1000x + 625

16x^4-160x^3+600x^2-1000x+625