How do you use the binomial formula to find expand #(2x+3)^3#?
1 Answer
Explanation:
The binomial formula that you need here is
#(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3#
Let me colour the same formula to add clarity:
#(color(red)(a) + color(blue)(b))^3 = color(red)(a^3) + 3color(red)(a^2)color(blue)(b) + 3color(red)(a)color(blue)(b^2) + color(blue)(b^3)#
In your case, you would like to expand
#a = 2x# and#b = 3#
Now, you need to plug
#(color(red)(2x)+color(blue)(3))^3 = color(red)((2x)^3) + 3* color(red)((2x)^2) * color(blue)(3) + 3 * color(red)(2x) * color(blue)(3^2) + color(blue)(3^3)#
# = (2x)^3 + 3 * (2x)^2 * 3 + 3 * (2x) * 3^2 + 3^3#
# = 2^3x^3 + 9 * 2^2x^2 + 3 * 2x * 9 + 27#
# = 8x^3 + 36x^2 + 54x + 27#