How do you use the binomial formula to find expand #(2x+3)^3#?

1 Answer
Feb 5, 2016

Answer:

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

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 #(color(red)(2x) + color(blue)(3))^3#, so your

#a = 2x# and #b = 3#

Now, you need to plug #2x# for every occurence of #a# in the formula and plug #3# for every occurence of #b# in the formula:

#(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#