The basic Number Properties (or laws) that apply to arithmetic operations are Commutative Property, Associative Property, Identity Property and Distributive Property.

The following table summarizes the number properties for addition and multiplication: Commutative, Associative, Distributive, Identity and Inverse. Scroll down the page for examples, explanations and solutions.

Distributive property allows you to remove the parenthesis (or brackets) in an expression. Multiply the value outside the brackets with each of the terms in the brackets.

For example: | 4(a + b) = 4a + 4b |

7(2c – 3d + 5) = 14c – 21d + 35 |

What happens if you need to multiply (*a* – 3)(*b* + 4)?

You do the same thing but with one value at a time.

For example:

Multiply *a* with each term to get *a* × *b* + 4 × *a* = *ab* + 4*a*

Then, multiply 3 with each term to get “ –3*b* – 12” (take note of the sign operations).

Put the two results together to get “*ab* + 4*a* – 3*b* – 12”

Therefore, (*a* – 3)(*b* + 4) = *ab* + 4*a* – 3*b* – 12

The following video shows more examples of the distributive property.

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