# How do you multiply 3x^2y^2z(7x^2+2y+z+4w)?

Apr 27, 2017

$21 {x}^{4} {y}^{2} z + 6 {x}^{2} {y}^{3} z + 3 {x}^{2} {y}^{2} {z}^{2} + 12 {x}^{2} {y}^{2} z w$

#### Explanation:

Multiply each part of $7 {x}^{2} + 2 y + z + 4 w$ by $3 {x}^{2} {y}^{2} z$
$3 {x}^{2} {y}^{2} z \left(7 {x}^{2}\right) = 21 {x}^{4} {y}^{2} z$
$3 {x}^{2} {y}^{2} z \left(2 y\right) = 6 {x}^{2} {y}^{3} z$
$3 {x}^{2} {y}^{2} z \left(z\right) = 3 {x}^{2} {y}^{2} {z}^{2}$
$3 {x}^{2} {y}^{2} z \left(4 w\right) = 12 {x}^{2} {y}^{2} z w$

Then you add each part to get
$21 {x}^{4} {y}^{2} z + 6 {x}^{2} {y}^{3} z + 3 {x}^{2} {y}^{2} {z}^{2} + 12 {x}^{2} {y}^{2} z w$