The number of terms in expansion of [(2x+3y)^4×(4x-6y)^4]^9 is

[(2x + 3y)⁴ * (4x –6y)⁴]⁹

we can write it as

 = [(2x + 3y)⁴ * 2⁴ (2x –3y)⁴]⁹

 = 2^{4 * 9} [(4x² –9y²)⁴]⁹

 = 2³⁶ [ 4x² –9y² ]³⁶

 

we know that in a binomial expansion of (a + b)ⁿ ,  there are (n + 1) terms

 

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