What are the 4 rules of algebraic expressions?
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Let a, b, and c be real numbers, variables, or algebraic expressions.
Commutative Property of AdditionWe can add numbers in any order.
Commmutative Property of MultiplicationWe can also multiply numbers in any order.
Associative Property of AdditionWe can group numbers in a sum any way we want and get the same answer.
Associative Property of MultiplicationWe can group numbers in a product any way we want and get the same answer.
Distributive PropertyWhen we are adding and multiplying with a parenthesis, we can distribute the multiplication through the addition.
For an in depth discussion, see Distributive Property
Additive Identity PropertyIf we add 0 to any number, we will end up with the same number.
Multiplicative Identity PropertyIf we multiply 1 to any number, we will end up with the same number.
Additive Inverse PropertyIf we adda number by the opposite of itself, we will end up with 0.
Multiplicative Inverse PropertyIf we multiply a number by its reciprocal, we will end up with 1.
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algebra rules for arithmetic
1 a(b+c)=ab+ac
2 a(bc)=abc
3 (ac)b=abc
4 a(bc)=acb
5 (ab)+(cd)=(ad+bc)bd
6 (a−b)(c−d)=(b−a)(d−c)
7 (a+b)c=ac+bc
8 ac+bcc=a+b
9 (ac)(bd)=adbc
1 a(b+c)=ab+ac
2 a(bc)=abc
3 (ac)b=abc
4 a(bc)=acb
5 (ab)+(cd)=(ad+bc)bd
6 (a−b)(c−d)=(b−a)(d−c)
7 (a+b)c=ac+bc
8 ac+bcc=a+b
9 (ac)(bd)=adbc
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