Why is the distributive property important?

Jan 9, 2015

The distributive property says that $a \left(b + c\right) = a \cdot b + a \cdot c$

Without this you wouldn't be able the expand expressions like:

$\left(x + 1\right) \left(2 x - 4\right)$ into

$x \left(2 x - 4\right) + 1 \left(2 x - 4\right)$, then

$x \cdot 2 x + x \cdot \left(- 4\right) + 1 \cdot 2 x + 1 \cdot \left(- 4\right)$ and then

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

In other words, you would not be able to 'clear the brackets'