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

Jul 17, 2015

$4 {x}^{2} - 9$

#### Explanation:

Split one of the brackets:
$\left(2 x + 3\right) \left(2 x - 3\right) = 2 x \left(2 x - 3\right) + 3 \left(2 x - 3\right)$

Split the remaining bracket:
$2 x \left(2 x\right) + 2 x \left(- 3\right) + 3 \left(2 x\right) + 3 \left(- 3\right) = 4 {x}^{2} - 6 x + 6 x - 9$

Combined the expanded terms:
$4 {x}^{2} - 9$

Jul 17, 2015

Alternatively, use the FOIL mnemonic to pick out pairs of terms to multiply from the two binomials...

#### Explanation:

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

$= {\underbrace{2 x \cdot 2 x}}_{\textcolor{b l u e}{\text{First")+underbrace(2x*-3)_color(blue)("Outside")+underbrace(3*2x)_color(blue)("Inside")+underbrace(3*-3)_color(blue)("Last}}}$

$= 4 {x}^{2} - \cancel{6 x} + \cancel{6 x} - 9$

$= 4 {x}^{2} - 9$

Or:
You could use the 'special product' of the form:
$\left(a + b\right) \left(a - b\right) = {a}^{2} - {b}^{2} \to$
$\left(2 x + 3\right) \left(2 x - 3\right) = {\left(2 x\right)}^{2} - {3}^{2} = 4 {x}^{2} - 9$