# What is the standard form of  y=(3x – 4) (2x – 1) (x – 2) ?

Feb 1, 2016

$6 {x}^{3} - 23 {x}^{2} + 26 x - 8$

#### Explanation:

$\left(3 x - 4\right) \left(2 x - 1\right) \left(x - 2\right)$

Writing this in Standard Form (of a polynomial) means that the terms are in order from highest to lowest degree (those tiny little numbers to the right of the $x$).

$\left(3 x - 4\right) \left(2 x - 1\right) \left(x - 2\right)$

a) Multiply $\left(3 x - 4\right)$ and $\left(2 x - 1\right)$*:
$\left(6 {x}^{2} - 3 x - 8 x + 4\right) \left(x - 2\right)$

• I combined (added) $- 3 x$ and $- 8 x$ to get $- 11 x$

b) Multiply $\left(6 {x}^{2} - 11 x + 4\right)$ and $\left(x - 2\right)$:
$6 {x}^{3} - 11 {x}^{2} + 4 x - 12 {x}^{2} + 6 x + 16 x - 8$

c) Rearrange terms into Standard Form:
$6 {x}^{3} - 11 {x}^{2} - 12 {x}^{2} + 4 x + 6 x + 16 x - 8$

d) Simplify:
$6 {x}^{3} - 23 {x}^{2} + 26 x - 8$

Notes:

• Due to the Associative Property of Multiplication, you can multiply these in any order you want to, I just usually go form left to right.
• I said to Multiply but this could be called FOILing or Distributing by your teacher
• You can always check the answer by factor it back out again because it is entirely possible that I had a multiplication, addition, or subtraction error along the way.