# How do you multiply  (7x)(8x) ?

Jun 26, 2015

$\left(7 x\right) \left(8 x\right) = 56 {x}^{2}$

#### Explanation:

$\left(7 x\right) \left(8 x\right) = \left(7 \cdot x\right) \cdot \left(8 \cdot x\right) = 7 \cdot x \cdot 8 \cdot x = 7 \cdot 8 \cdot x \cdot x$

$= \left(7 \cdot 8\right) \cdot \left(x \cdot x\right) = 56 {x}^{2}$

using commutativity and associativity of multiplication.

That is, for any $a$, $b$ and $c$:

$a \cdot b = b \cdot a$

and

$a \cdot \left(b \cdot c\right) = \left(a \cdot b\right) \cdot c$