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

To find the cube of $\left(2 b + 6 x\right)$, 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:

$1 \left(2 b\right) \left(6 x\right) + 3 \left(2 b\right) \left(6 x\right) + 3 \left(2 b\right) \left(6 x\right) + 1 \left(2 b\right) \left(6 x\right)$

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:

$1 {\left(2 b\right)}^{3} {\left(6 x\right)}^{0} + 3 {\left(2 b\right)}^{2} {\left(6 x\right)}^{1} + 3 {\left(2 b\right)}^{1} {\left(6 x\right)}^{2} + 1 {\left(2 b\right)}^{0} {\left(6 x\right)}^{3}$

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!)

$8 {b}^{3} + 72 {b}^{2} {x}^{1} + 216 {b}^{1} {x}^{2} + 216 {x}^{3}$

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