# How do you use the Binomial Theorem to expand (2x+3)^3?

Nov 14, 2016

$8 {x}^{3} + 36 {x}^{2} + 54 x + 27$

#### Explanation:

Binomial expansion of ${\left(x + a\right)}^{n}$ is written as follows

= x^n + nax^(n-1)+ (n(n-1))/(2!) a^2 x^(n-2) +(n(n-1)(n-2))/(3!)a^3 x^(n-3)+......

To write the binomial expansion of ${\left(2 x + 3\right)}^{3}$ can be written using the above expression by substituting 2x for x and 3 for a and of course n=3

Accordingly the required expansion would be :
 (2x)^3 +3*3*(2x)^2 +(3*2)/(2!) 3^2 (2x) +(3*2*1)/(3!) 3^3(2x)^0

=$8 {x}^{3} + 36 {x}^{2} + 54 x + 27$