# How do you multiply (3x-4) (4x+3)?

Jun 26, 2015

$\left(3 x - 4\right) \left(4 x + 3\right)$

$= 3 x \left(4 x + 3\right) - 4 \left(4 x + 3\right)$

$= 12 {x}^{2} + 9 x - 16 x - 12$

$= 12 {x}^{2} - 7 x - 12$

#### Explanation:

This is like the reverse of factoring by grouping, using the distributive property of multiplication...

$\left(3 x - 4\right) \left(4 x + 3\right)$

$= 3 x \left(4 x + 3\right) - 4 \left(4 x + 3\right)$

$= \left(3 x \cdot 4 x\right) + \left(3 x \cdot 3\right) - \left(4 \cdot 4 x\right) - \left(4 \cdot 3\right)$

$= 12 {x}^{2} + 9 x - 16 x - 12$

$= 12 {x}^{2} + \left(9 - 16\right) x - 12$

$= 12 {x}^{2} - 7 x - 12$