Read : a2 b2 formula , Hello friends, in today’s article we will give you information about a² b² formulas. We need these formulas while solving maths problems. There are many students who have difficulty in these formulas and they are not able to solve the questions.
So in this article we will give you information about all the formulas of a² b². To understand the formulas, many examples have been given to you, from which you can learn to formulate. So let’s know what are a² b² formulas and how are they applied ?
a2 b2 formula
Algebra Formulas
- (a + b)² = a² + 2ab + b²
- (a – b)² = a² – 2ab + b²
- (a – b)² = (a + b)² – 4ab
- (a + b)² = (a – b)² + 4ab
- a² + b² = (a + b)² – 2ab
- a² + b² = (a – b) + 2ab
- a² – b² = (a + b) (a – b)
(a + b)² Formula
We use a² + b² to solve problems in mathematics. We can express (a + b)² in two ways. It is as follows-
- (a + b)² = a² + 2ab + b²
- (a + b)² = (a – b)² + 4ab
This formula is very easy to solve. Below we have explained how to solve this formula-
- (a + b)² = (a + b)(a + b)
- (a + b)² = a² + ab + ba + b²
- (a + b)² = a² + 2ab + b²
How to use (a + b)² Formula
Now we will learn to use A²+B² formula. You can use any of the formulas from both the sutras. The value of both will come equal. Below you are given examples of this formula so that you can learn to solve the question-
Example -1 Using sum of squares formula, find the value of (6 + 5)² ?
Ans-
Type-1
find : value of (6 + 5)²
Given: a = 6, b = 5
Using (a + b)² Formula
(a + b)² = a² + 2ab + b²
(6 + 5)² = (6)² + 2 (6)(5) + (5)²
= 36 + 60+ 25
= 121
Type-2
find : value of (6 + 5)²
Given: a = 6, b = 5
Using (a + b)² Formula
(a + b)² = (a – b)² + 4ab
(6 + 5)² = 1 + 4 (6)(5)
= 1 + 120
= 121
Example -2 Using sum of squares formula, find the value of (4 + 3)² ?
Ans-
Type-1
find : value of (4 + 3)²
Given: a = 4, b = 3
Using (a + b)² Formula
(a + b)² = a² + 2ab + b²
(4 + 3)² = (4)² + 2 (4)(3) + (3)²
= 16 + 24+ 9
= 49
Type-2
find : value of (4 + 3)²
Given: a = 4, b = 3
Using (a + b)² Formula
(a + b)² = (a – b)² + 4ab
(6 + 5)² = 1 + 4 (4)(3)
= 1 + 48
= 49
(a – b)² Formula
We use a² + b² to solve problems in mathematics. We can express (a – b)² in two ways. It is as follows-
- (a – b)² = a² – 2ab + b²
- (a – b)² = (a + b)² – 4ab
This formula is very easy to solve. Below we have explained how to solve this formula-
- (a – b)² = (a + b)(a + b)
- (a – b)² = a² – ab – ba + b²
- (a – b)² = a² – 2ab + b²
How to use (a – b)² Formula
Now we will learn to use A²+B² formula. You can use any of the formulas from both the sutras. The value of both will come equal. Below you are given examples of this formula so that you can learn to solve the question –
Example -1 Using sum of squares formula, find the value of (6 – 5)² ?
Ans-
Type-1
find : value of (6 – 5)²
Given: a = 6, b = 5
Using (a – b)² Formula
(a – b)² = a² – 2ab + b²
(6 – 5)² = (6)² – 2 (6)(5) + (5)²
= 36 – 60+ 25
= 1
Type-2
find : value of (6 – 5)²
Given: a = 6, b = 5
Using (a – b)² Formula
(a – b)² = (a + b)² – 4ab
(6 – 5)² = (6 + 5)² – 4(6)(5)
= 121 – 120
= 1
Example -2 Using sum of squares formula, find the value of (5 – 3)² ?
Ans-
Type-1
find : value of (5 – 3)²
Given: a = 5, b = 3
Using (a – b)² Formula
(a – b)² = a² – 2ab + b²
(5 – 3)² = (5)² – 2 (5)(3) + (3)²
= 25 – 30+ 9
= 4
Type-2
find : value of (5 – 3)²
Given: a = 5, b = 3
Using (a – b)² Formula
(a – b)² = (a + b)² – 4ab
(5 – 3)² = (5 + 3)² – 4 (5)(3)
= 64 – 60
= 4
a² + b² Formula
We use a² + b² to solve problems in mathematics. We can express a² + b² in two ways. It is as follows-
- a²+b² = (a+b)² – 2ab
- a²+b² = (a+b)² + 2ab
We can also prove this formula. If you want to prove this formula, then you have to do LHS = RHS. Both these formulas are proofed below-
Type – 1
Prove that “a²+b² = (a+b)² – 2ab”
a²+b² = (a-b)² + 2ab
a²+b² = a²-2ab+b²+2ab
a²+b² = a²+b²
LHS = RHS
Hence, “a²+b² = (a+b)² – 2ab”
Type – 2
a²+b² = (a-b)² + 2ab
a²+b² = a²-2ab+b²+2ab
a²+b² = a²+b²
LHS = RHS
How to use a²+b² Formula
Now we will learn to use A²+B² formula. You can use any of the formulas from both the sutras. The value of both will come equal. Below you are given examples of this formula so that you can learn to solve the question-
Example 1: Using sum of squares formula, find the value of 6² + 5² ?
Ans-
Type-1
find : value of 6² + 5²
Given: a = 6, b = 5
Using a²+b² Formula
a² + b² = (a + b)² − 2ab
6² + 5² = (6 + 5)² − 2(6)(5)
= 121 − 2(30)
= 121 − 60
= 61
Type-2
find : value of 6² + 5²
Given: a = 6, b = 5
Using a²+b² Formula
a² + b² = (a-b)² + 2ab
6² + 5² = (6 – 5)² + 2(6)(5)
= 1 + 2(30)
= 1 + 60
= 61
Example 2: Using sum of squares formula, find the value of 4² + 3² ?
Ans-
Type-1
find : value of 4² + 3²
Given: a = 4, b = 3
Using a²+b² Formula
a² + b² = (a + b)² − 2ab
4² + 3² = (4 + 3)² − 2(4)(3)
= 49 − 2(12)
= 49 − 24
= 21
Type-2
find : value of 4² + 3²
Given: a = 4, b = 3
Using a²+b² Formula
a² + b² = (a-b)² + 2ab
a² + b² = (a – b)² + 2ab
4² + 3² = (4 – 3)² + 2(4)(3)
= 1 + 2(12)
= 1 + 24
= 25
a² – b² Formula
We use a² – b² to solve problems in mathematics. It is as follows-
a² – b² = (a + b) (a – b)
How to use a² – b² Formula
Now we will learn to use a² – b² formula. Below you are given examples of this formula so that you can learn to solve the question-
Example 1: Using sum of squares formula, find the value of 6² – 5² ?
Ans-
find : value of 6² – 5²
Given: a = 6, b = 5
Using a² – b² Formula
a² – b² = (a + b) (a – b)
6² – 5² = (6 + 5) (6 – 5)
= (11) (1)
= 11
Example 2: Using sum of squares formula, find the value of 5² – 3² ?
Ans-
find : value of 5² – 3²
Given: a = 5, b = 3
Using a² – b² Formula
a² – b² = (a + b) (a – b)
5² – 3² = (5 + 3) (5 – 3)
= (8) (2)
= 16
What is algebra?
Algebra began with calculations similar to arithmetic. In which letters came for numbers. It allowed proof of those assets. It can contain any number. For example, in the quadratic equation
ax² + bx + c = 0,
a,b,c can be any number. The quadratic formula can be used to quickly and easily find the values of unknown quantities. which finds all the solutions of the equation.
Historically and in current teaching, the study of algebra begins with solving equations such as the quadratic equation above. Then more general questions, such as ‘Does an equation have any solution?’, ‘How many solutions does an equation have?’, ‘What can be said about the nature of the solutions?’ are considered.
These questions have expanded algebra to non-numerical objects, such as permutations, vectors, matrices, and polynomials. The structural properties of these non-numeric objects were then abstracted into algebraic structures such as groups, rings, and fields.
Before the 16th century, mathematics was divided into only two subfields, arithmetic and geometry. Some methods that were developed long ago can today be considered algebra. After the emergence of algebra in the 16th or 17th century, there are infinitesimal calculus as subfields of mathematics.
From the late 19th century, many new areas of mathematics emerged, most using both arithmetic and geometry, and almost all using algebra.
Today algebra has evolved to include many branches of mathematics, as can be seen in mathematics subject classification. Where none of the first level fields (two-digit entries) are called algebra.
Today algebra includes sections 08-General Algebraic Systems, 12- Field Theory and Polynomials, 13- Commutative Algebra, 15- Linear and Polylinear Algebra, Matrix Theory, 16-Associative Rings and Algebra, 17- Non-Associative Rings and Algebra, 18- Category Theory, Homologous Algebra, 19- K-Theory and 20- Group Theory. Algebra is widely used in 11- number theory and 14- algebraic geometry.
FAQ
1. What Is the Expansion of a² + b² Formula ?
Ans- We can express a² + b² in two ways. It is as follows-
a²+b² = (a+b)² – 2ab
a²+b² = (a+b)² + 2ab
2. What Is the Expansion of (a + b)² Formula ?
Ans- We can express (a + b)² in two ways. It is as follows-
(a + b)² = a² + 2ab + b²
(a + b)² = (a – b)² + 4ab
3. What Is the Expansion of (a – b)² Formula ?
Ans- We can express (a – b)² in two ways. It is as follows-
(a – b)² = a² – 2ab + b²
(a – b)² = (a + b)² – 4ab
4. What Is the Expansion of a² – b² Formula ?
Ans- a² – b² = (a + b) (a – b)
Conclusion
In this article, you have been given examples along with the sources. There are some formulas which can be solved in two ways. You can solve the question in any way you like.
From this article, you must have learned how to apply algebra formulas. If you have any doubt related to this article then you can ask in comment, your doubt will be cleared.
If you liked this article, then share it with your friends so that they can also know about these formulas and solve the questions.
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