How do you multiply 3 ( x − 7 ) ( x + 2 ) ( 2 x − 1 ) ?

Sep 21, 2015

$= 6 {x}^{3} - 33 {x}^{2} - 69 x + 42$

Explanation:

There's really no shortcut to this. You will have to multiply each factor one by one. I suggest you multiply the factor $3$ last since that's the easiest. Start with any two from the three binomial factors.

$3 \left(x - 7\right) \left(x + 2\right) \left(2 x - 1\right)$
$= 3 \left(x - 7\right) \left(2 {x}^{2} + 4 x - x - 2\right)$
$= 3 \left(x - 7\right) \left(2 {x}^{2} + 3 x - 2\right)$
$= 3 \left(2 {x}^{3} + 3 {x}^{2} - 14 {x}^{2} - 2 x - 21 x + 14\right)$
$= 3 \left(2 {x}^{3} - 11 {x}^{2} - 23 x + 14\right)$

$= 6 {x}^{3} - 33 {x}^{2} - 69 x + 42$