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Algebra Formulas- Algebra formulae are the fundamental formulae used to simplify algebraic statements. Algebraic formulas serve as the foundation for solving a wide range of complicated problems. Algebraic formulas are useful for resolving algebraic, quadratic, polynomials, trigonometrics, probability, and more.
Algebra Formulas
An identity is an equation that holds true in every way for any values provided to the variables. Algebraic identities are utilised to solve various equations. For algebraic identities, L.H.S is always equal to R.H.S.
Algebraic Identities
Some important algebraic identities are
(a + b)2 | a2 + b2 + 2ab |
(a – b)2 | a2 + b2 – 2ab |
(a + b)(a – b) | a2 – b2 |
(x + a)(x + b) | x2 + x(a + b) + ab |
What are Algebra Formulas?
Algebraic formulae are equations that need an algebraic expression on both sides of the “equal to” operator, i.e. on both the left and right sides. Algebraic formulae are typically true across all values. Algebraic formulas simplify algebraic equations and are used to solve a variety of mathematical issues. This article will cover algebraic formulae for various classes.
Algebraic properties
- Addition’s Commutative property: a + b = b + a
If the order of the elements is modified, the sum of the expression does not change. Expressions or numbers can be used as elements.
- Multiplication’s Commutative Property: a x b = b x a
The product does not change when the order of the factors is changed. Numbers or phrases can be used as these factors.
- Addition’s Associative Property: (a + b)+ c = a + (b + c)
The property states that when two or more numbers are brought together to execute essential arithmetic addition, the order of the numbers has no bearing on the outcome.
- Multiplication has an associative property: (a x b) xc = a x (b x c)
When two or more factors are joined together in basic arithmetical multiplication, the order of the elements does not affect the final result. Also, in this situation, parenthesis is used to organise the items.
- Addition and Multiplication have distributive properties:
a × (b + c) = a × b + a × c and (a + b) × c = a × c + b × c
The distributive property states that multiplying each element by a single term and then adding and subtracting the products is the same as multiplying each component by a single term and then adding and subtracting the products.
- Rule of multiplication over subtraction: p (q-r) = p*q – p*r
If p, q, and r, are all integers. Likewise, you can use the left and right distributions in the addition rule for Multiplication over subtraction.
Left distributive law if p* (q-r) = (p * q) – (p*r)- and
Right distributive law if (p-q)*r = (p*r) – (q*r)-
Intricate knowledge of Algebra makes you think logically and solve complex mathematical problems efficiently. Algebraic identities are applicable in various branches of mathematics, including Algebra, Geometry, and Trigonometry.
Important Formulas in Algebra
The section has listed all algebra formulas to resolve the fundamental and complicated Mathematical problems for secondary standard students.
The basic formulae
- 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 + 2bc + 2ca
- (a – b – c)2 = a2 + b2 + c2 – 2ab + 2bc – 2ca
- (a + b)3 = a3 + 3a2b + 3ab2 + b3 ; (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3 = a3 – b3 – 3ab(a – b)
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (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)
- If n is a natural number an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
- If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
- If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….)
- Laws of Exponents (am)(an) = am+n ; (ab)m = ambm ; (am)n = amn
Algebra Formulas for Class 8
This article discusses algebra formulae for class 8. The algebraic formulae for three variables a, b, and c are as follows:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b)(a – b) = a2 – b2
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- a3 + b3 = (a + b)(a2 – ab + b2)
- a3 – b3 = (a – b)(a2 + ab + b2)
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Algebra Formulas for Class 9
Formulas for logarithms are quite important in class 9. They are useful for computing complicated multiplication and division issues. The exponential form of 32 = 9 may be readily converted to logarithmic form as log 3 9 = 2. Furthermore, complex multiplication and division may be simply transformed to addition and subtraction using logarithmic formulae.
The following are some of the most frequent log algebraic formulas:
- loga (xy) = loga x + loga y
- loga (x/y) = loga x – loga y
- loga xm = m loga x
- loga a = 1
- loga 1 = 0
- am× an = am + n
- am/an = am – n
- (am)n = amn
- (ab)m = am× bm
- a0 = 1
- a-m = 1/am
Algebra Formula Solved Examples
Example 1: Find out the value of the term, (5x + 4)2 using algebraic formulae.
Solution: Using the algebraic formula,
(a + b)2 = a2 + b2 + 2ab
(5x + 4)2 = (5x)2 + 42 + 2 × 5x × 4
(5x + 4)2 = 25x2 + 16 + 40x
Example 2: Find out the value of the term, (9x – 5y)2 using algebraic formulae.
Solution: Using the algebraic formula,
(9x – 5y)2 = (9x)2 + (5y)2 – 2 × 9x × 5y
(9x – 5y)2 = 9x2 + 25y2 – 90xy
Example 3: Find out the value of, 205×195 using algebraic formulae.
Solution: Using the algebraic formula,
(a + b)(a – b) = a2 – b2
205×195 = (200+5)(200-5)
= 2002 – 52
= 40000 – 25
= 39975
FAQs (Frequently Asked Questions)
1. Where can I get all the Algebra Formulas?
You will find all the Algebra formulas on Extramarks.
2. What is the general formula in Algebra?
The general algebra formulas that are used are given below:
- (a + b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- (a + b)(a – b) = a2 – b2
3. How to remember and implement the Algebra formulas?
As academic experts suggest, one of the best ways to remember algebra formulas is to practice and revise them consistently.
4. What are Algebraic Expressions?
Algebraic expressions combine variables and constants using arithmetic operations including addition, subtraction, multiplication, and division.