# How do you multiply (9x ^ { 3} - 8) ( x ^ { 9} - 3)?

Dec 3, 2017

$= 9 {x}^{12} - 8 {x}^{9} - 27 {x}^{3} + 24$

#### Explanation:

Follow the FOIL rule (First, Outer, Inner, Last)

$\left(9 {x}^{3} - 8\right) \left({x}^{9} - 3\right)$

Note: When dealing with exponents, follow the exponent laws.

$\left(9 {x}^{3} \cdot {x}^{9}\right) + \left(9 {x}^{3} \cdot - 3\right) + \left(- 8 \cdot {x}^{9}\right) + \left(- 8 \cdot - 3\right)$

Note: (negative) $\cdot$ (negative) = (positive)

$\left(9 {x}^{3 + 9}\right) + \left(- 27 {x}^{3}\right) + \left(- 8 {x}^{9}\right) + \left(24\right)$

$9 {x}^{12} - 27 {x}^{3} - 8 {x}^{9} + 24$

I'm just going to rearrange it in descending order of x

$= 9 {x}^{12} - 8 {x}^{9} - 27 {x}^{3} + 24$