33 lines
670 B
Markdown
33 lines
670 B
Markdown
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---
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tags:
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- theorems
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- prealgebra
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---
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# The Distributive Property of Multiplication
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**Let $a$, $b$ represent members of $\mathbb{W}$ or $\mathbb{Z}$ then:**
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$$ a \cdot (b + c) = a \cdot b + a \cdot c $$
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### Demonstration
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When faced with $4(2\cdot3)$ we may proceed with the official order of
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operations in algebra, namely:
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```
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4 x (2 + 3) = 4 x (5)
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= 20
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```
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In other words we find the sum of the values in parentheses and then multiply
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this by the value outside of the brackets.
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When we use distributive property we _distribute_ each value in the parentheses
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against the value outside of the parentheses:
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```
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4 x (2 + 3) = (4 x 2) + (4 x 3)
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8 + 12 = 20
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```
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