# How do you find the product of (3a-b)(2a-b)?

May 2, 2018

Multiply each term in the parenthesis by each term in the other parenthesis, or better known as the FOIL method.

#### Explanation:

$\left(3 a - b\right) \left(2 a - b\right)$

$= \left(3 a\right) \left(2 a\right) + \left(3 a\right) \left(- b\right) + \left(- b\right) \left(2 a\right) + \left(- b\right) \left(- b\right)$

$= 6 {a}^{2} + {b}^{2} - 5 a b$

May 2, 2018

Formally, $\left(a + b\right) \cdot \left(c + d\right) = a c + a d + b c + b d$.
When there are negative signs or subtraction involved, it may be helpful to re-write the equation in standard form.

#### Explanation:

$\left(3 a - b\right) \left(2 a - b\right) =$
$\left(3 a + - b\right) \left(2 a + - b\right) =$
$\left(3 a \cdot 2 a\right) + \left(3 a \cdot - b\right) + \left(- b \cdot 2 a\right) + \left(- b \cdot - b\right) =$
$6 {a}^{2} + \left(- 3 a b\right) + \left(- 2 a b\right) + \left({b}^{2}\right) =$
$6 {a}^{2} - 5 a b + {b}^{2}$

May 2, 2018

3a times -b; 3a times 2a
-b times 2a; -b times -b
This should get you $6 {a}^{2} - 5 a b + {b}^{2}$ as your product.