# How do you multiply (3x+1)(x-2)?

Jul 4, 2015

Multiply each term in one factor time each term in the other factor

#### Explanation:

We need to multiply: $3 x$ times $x$ and times $- 2$ and we need to multiply $1$ times $x$ and times $- 2$.

We can (but are not required to) write:

$\left(3 x + 1\right) \left(x - 2\right) = \left(3 x \cdot x\right) + \left(3 x \cdot - 2\right) + \left(1 \cdot x\right) + \left(1 \cdot - 2\right)$

We get:

$\left(3 x + 1\right) \left(x - 2\right) = 3 {x}^{2} + \left(- 6 x\right) + x + \left(- 2\right)$

which is also equal to
$\left(3 x + 1\right) \left(x - 2\right) = 3 {x}^{2} - 6 x + x - 2$

Now simplify by combining like terms ($- 6 x + x = - 5 x$)

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