Why is the distributive property important?

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Answer 1 · 2015-01-09T11:56:18

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

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

$(x + 1) (2 x - 4)$ $(x+1)(2x-4)$ into

$x (2 x - 4) + 1 (2 x - 4)$ $x(2x-4)+1(2x-4)$ , then

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

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

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