# Formulas For Algebra

## Algebra Formulas:-

Definition:

Algebra is the study of mathematical symbols. It also comprises of the rules that are used to manipulate these symbols. The study comprises of almost everything from elementary equation solving to the study of abstractions such as groups, rings, and fields.

## Formulas for Algebra:

• a2 – b2 = (a – b)(a + b)
• (a+b)2 = a2 + 2ab + b2
• a2 + b2 = (a – b)2 + 2ab
• (a – b)2 = a2 – 2ab + b2
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
• (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
• (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• a3 – b3 = (a – b)(a2 + ab + b2)
• a3 + b3 = (a + b)(a2 – ab + b2)
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3
• (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
• (a – b)4 = a4 – 4a3b + 6a2b2 – 4ab3 + b4)
• a4 – b4 = (a – b)(a + b)(a2 + b2)
• a5 – b5 = (a – b)(a4 + a3b + a2b2 + ab3 + b4)

## Algebra Formulas & Properties of Algebra:

a + b = b + a
The sum of the expression does not changes if the order of the elements are changed. The elements can be expressions or numbers.

### 2.Commutative Property of Multiplication:

a x b = b x a
When the order of the factors are changed, the product does not change. These factors can be numbers or expressions

### 3. Associative Property of Addition:

(a + b)+ c = a + (b + c)
The property defines that when two or more numbers are grouped together which are performing basic arithmetic addition, their order does not play a significant role in the result. The grouping is usually done by placing the parenthesis.

### 4. Associative property of Multiplication:

(a x b) xc = a x (b x c)
Associative property states that when two or more elements are grouped together in the basic arithmetical multiplication, their order does not change the final result. Also, in this case, the grouping is usually done by parenthesis.

### 5. Distributive properties of Addition and Multiplication:

a × (b + c) = a × b + a × c and (a + b) × c = a × c + b × c.
The distributive property says that the product of a single term and a sum or a difference of two or more terms present in the bracket is same as multiplying each of the element by a single term and them adding and subtracting the products.

### 6. Rule of multiplication over subtraction:

If p, q, and r are any numbers, then, p (q-r) = p*q – p*r. Similarly, in the addition rule, the distribution for multiplication over subtraction can be done in left distribution and right distribution.

If p* (q-r) = (p * q) – (r*q)- Left distributive law
If (p-q)*r = (p*r) – (q*r)- Right distributive law

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