How many terms are in the binomial expansion of (2x+3) ^3

There are 6 terms because when you see a power after a monomials or polynomial, it means it is the same things multiplied to it x number of times. So if it is to the power of 3 it is (2x+3) (2x+3) (2x+3). This is 6 terms

(2 x + 3) 3 = 8 x 3 + 36 x 2 + 54 x + 27

Step-by-step explanation:

(a + b) 2 = 1 ⋅ a 2 ⋅ b 0 + 2 ⋅ a 1 ⋅ b 1 + 1 ⋅ a 0 ⋅ b 2

Then : (a + b) 2 = a 2 + 2 a b + b 2

To the power 3 : (a + b) 3 = 1 ⋅ a 3 ⋅ b 0 + 3 ⋅ a 2 ⋅ b 1 + 3 ⋅ a 1 ⋅ b 2 + 1 ⋅ a 0 ⋅ b 3 Then (a + b) 3 = a 3 + 3 a 2 b + 3 a b 2 + b 3

So here we have a = 2 x and b = 3 : And (2 x + 3) 3 = (2 x) 3 + 3 ⋅ (2 x) 2 ⋅ 3 + 3 ⋅ (2 x) ⋅ 3 2 + 3 3

Therefore : (2 x + 3) 3 = 8 x 3 + 36 x 2 + 54 x + 27