Simplifying Algebraic Expressions Using Distributive Property Posulate: Example With Ab + Bc + Ac

______ ______ posulate ab+ bc+ ac

segement addition

The distributive property posulate is what can be applied to simplify the given expression: ab + bc + ac.

Distributive property posulate states that when a number or a variable is multiplied by a sum or a difference of two or more numbers or variables, it can be distributed or split among those numbers or variables by multiplying it with each one individually, and then adding or subtracting them. Mathematically, it can be represented as:

a(b + c) = ab + ac
or
a(b – c) = ab – ac

By using the distributive property posulate, we can simplify the given expression as follows:

ab + bc + ac
= a(b + c) + bc (applying distributive property for the first two terms)
= a(b + c) + b(c + a) (rearranging the terms)
= a(b + c) + b(a + c) (rearranging the terms again)
= ab + ac + ba + bc (applying the distributive property again)
= ab + ba + ac + bc (rearranging the terms)
= (a + b) (b + c) (applying the distributive property for the last time)

Therefore, the simplified form of the given expression is (a + b) (b + c).

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