How do I find the cube of #(2b + 6x)#?

To find the cube of #(2b +6x)#, the most efficient method would be to use binomial expansion by means of Pascal's Triangle.

To begin, Pascals Triangle is as follows:

Because you want to find the cube of the binomial, take the coefficients from row 3 and write them out with spaces in between as follows:

1...............3...............3...............1

Now, take each part of the binomial (the 2b and the 6x), and put each term in it's own set of brackets after each coefficient as follows:

#1(2b)(6x)+3(2b)(6x)+3(2b)(6x)+1(2b)(6x)#

Now, add exponents to the "b"s, starting with 3 and counting down to 0, then add exponents to the "x"s, starting with 0 and counting up to 3 like so:

#1(2b)^3(6x)^0+3(2b)^2(6x)^1+3(2b)^1(6x)^2+1(2b)^0(6x)^3#

Now simplify everything! (Find the coefficients by simplyifying exponents first, then doing multiplication. Then, do the count down-count up method with the exponents on the variables!)

#8b^3+72b^2x^1+216b^1x^2+216x^3#

That's all there is to it! Hopefully you've understood this and hopefully I was of some help! :)