# How do I find the cube of (4 x - 5b)?

Sep 18, 2014

I use Pascal's Triangle to expand binomials when I don't want to do the Distributive Property over and over again.
The pattern looks like:

The row we need for cubing is 1, 3, 3, 1.
Use those as the coefficients for each term, and descend the powers of 4x as you ascend the powers of -5b:

$1 {\left(4 x\right)}^{3} + 3 {\left(4 x\right)}^{2} \left(- 5 b\right) + 3 \left(4 x\right) {\left(- 5 b\right)}^{2} + 1 {\left(- 5 b\right)}^{3}$

Now, follow the order of operations by completing the exponents first:

$1 \left(64 {x}^{3}\right) + 3 \left(16 {x}^{2}\right) \left(- 5 b\right) + 3 \left(4 x\right) \left(25 {b}^{2}\right) + 1 \left(- 125 {b}^{3}\right)$

And last, some multiplications:

$64 {x}^{3} - 240 {x}^{2} b + 300 x {b}^{2} - 125 {b}^{3}$

Phew!