Question

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

Answer 1

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

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

Answer 2

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