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

Jul 21, 2018

${x}^{2} - 5 x + 6$

#### Explanation:

We can use the highly useful mnemonic FOIL (Firsts, Outsides, Insides, Lasts). This is the order we multiply in. We get

• Multiply the first terms: $x \cdot x = {x}^{2}$
• Multiply the outside terms: $x \cdot - 3 = - 3 x$
• Multiply the inside terms: $- 2 \cdot x = - 2 x$
• Multiply the last terms: $- 2 \cdot - 3 = 6$

Putting it all together, we get

${x}^{2} - 3 x - 2 x + 6$, or ${x}^{2} - 5 x + 6$

Hope this helps!

${x}^{2} - 5 x + 6$

#### Explanation:

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

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

$= {x}^{2} - 2 x - 3 x + 6$

$= {x}^{2} - 5 x + 6$