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➡➡ Give all formula of polynomial and real numbers
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The Three Defining Properties of Real Numbers
For all real numbers a, b and c, the following properties hold true.
1. The commutative property:
a + b = b + a
ab = ba
2. The associative property:
a + (b + c) = (a + b) + c
a(bc) = (ab)c
3. The distributive property:
a(b + c) = ab + ac
These properties define (almost) all other facts about real numbers, and chief among them are the
formulas we give below.
Remember that the distributive property is an equality between two expressions. Going from the
left expression to the right expression is called distributing a over the sum b + c, while going from
the right expression to the left expression is called factoring a out, and a is called the common
factor of ab and ac.
2 Important Formulas
Here are the factoring formulas you should know by now: for any real numbers a and b,
(a + b) 2 = a 2 + 2ab + b 2 Square of a Sum
(a − b) 2 = a 2 − 2ab + b 2 Square of a Difference
a 2 − b2 = (a − b)(a + b) Difference of Squares
a 3 − b3 = (a − b)(a 2 + ab + b 2 ) Difference of Cubes
a 3 + b 3 = (a + b)(a 2 − ab + b2 ) Sum of Cubes
For all real numbers a, b and c, the following properties hold true.
1. The commutative property:
a + b = b + a
ab = ba
2. The associative property:
a + (b + c) = (a + b) + c
a(bc) = (ab)c
3. The distributive property:
a(b + c) = ab + ac
These properties define (almost) all other facts about real numbers, and chief among them are the
formulas we give below.
Remember that the distributive property is an equality between two expressions. Going from the
left expression to the right expression is called distributing a over the sum b + c, while going from
the right expression to the left expression is called factoring a out, and a is called the common
factor of ab and ac.
2 Important Formulas
Here are the factoring formulas you should know by now: for any real numbers a and b,
(a + b) 2 = a 2 + 2ab + b 2 Square of a Sum
(a − b) 2 = a 2 − 2ab + b 2 Square of a Difference
a 2 − b2 = (a − b)(a + b) Difference of Squares
a 3 − b3 = (a − b)(a 2 + ab + b 2 ) Difference of Cubes
a 3 + b 3 = (a + b)(a 2 − ab + b2 ) Sum of Cubes
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