Expand $(2x+3)^3$ using binomial expansion?

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Answer 1 · 2017-04-28T16:49:39

$(2x+3)^3=8x^3+12x^2+54x+27$

Binomial expansion of $(a+b)^n=C_0^na^n+C_1^na^(n-1)b+C_2^na^(n-2)b^2+C_3^na^(n-3)b^3+..++C_n^n)b^n$

where $C_r^n=(n(n-1)(n-2).....(n-r+1))/(1.2.3.....r)$ and $C_0^n=1$

Hence $(2x+3)^3$

= $C_0^3(2x)^3+C_1^3(2x)^(3-1)3+C_2^3(2x)^(3-2)3^2+C_3^3(2x)^(3-3)3^3$

= $(2x)^3+3/1(2x)^2xx3+(3xx2)/(1xx2)(2x)9+(3xx2xx1)/(1xx2xx3)(2x)^0xx27$

= $8x^3+12x^2+54x+27$

Expand (2x+3)^3(2x+3)^3 using binomial expansion?