A^2 - b^2 Formula - Examples | A Square - B Square Formula?

There are two a 2 b 2 formulas that are, a 2 + b 2 , and a 2 – b 2 the expansion formula for a 2 b 2 formulas are given as, a 2 – b 2 = (a + b)(a – b) a 2 + b 2 = (a + b) 2 – 2ab.

What is an example of a2 b2 c2?

Pythagorean triples: A Pythagorean triple is a set of three positive whole numbers a, b, and c, such that a2 + b2 = c2. In other words, the numbers in a Pythagorean triple represent the lengths of the sides of a right triangle. For example, {3, 4, 5} is a well-known Pythagorean triple.

What is the a2 + b2 formula?

What is the a² - b² Formula in Algebra? Ans. The formula of a² - b² is a² - b² = (a + b) (a - b) .

What is the formula for a2+ b2 c2?

The a 2 + b 2 + c 2 formula is used to find the sum of squares of three numbers without actually calculating the squares. It says a 2 + b 2 + c 2 = (a + b + c) 2 - 2ab - 2bc - 2ca .

What is the formula of 2 into a square b square?

2(a²+b²)=(a+b)²+(a-c)(a+c)+(b-c)(b+c)-2(ab-c²) .

What are 2 examples of Pythagorean Theorem?

Pythagorean triples In other words, a Pythagorean triple represents the lengths of the sides of a right triangle where all three sides have integer lengths. Such a triple is commonly written (a, b, c). Some well-known examples are (3, 4, 5) and (5, 12, 13) .

How to work out a2, b2, c2?

The Pythagorean Theorem describes the relationship among the three sides of a right triangle. In any right triangle, the sum of the areas of the squares formed on the legs of the triangle equals the area of the square formed on the hypotenuse : a2 + b2 = c2.

Is the equation a2 b2 c2 true for every triangle?

Pythagorean theorem: If a triangle is a right triangle (has a right angle), then a2+b2=c2 . Converse: If a2+b2=c2 in a triangle with c is the longest side, then a triangle is a right triangle. If a triangle is not a right triangle, there are 2 other options for types of triangles.

Who created the equation a2 b2 c2?

Pythagoras was a teacher and a philosopher. Pythagoras found out that for a right angle triangle (with one of the angles being 90 o ), the square of the hypotenuse is equal to the sum of the squares of the other two sides: a 2 +b 2 =c 2 .

What is the square formula with example?

What Is the Squaring Formula in Math? In math, the square formula calculates the square of any number, square of a = a 2 = a × a , such as the square of 5 is 5 × 5 = 25. We can clearly see that the square and the square root of any number are inverse operations.

What is the use of a b2 formula in real life?

What is the use of (A +B) 2 in real life? In real life, the formula (a + b)² is used to find the area of a square by squaring the sum of its sides .

What is the square B square rule?

Ans. a 2 + b 2 formula is known as the sum of squares formula; it is read as a square plus b square. Its expansion is expressed as a 2 + b 2 = (a + b) 2 -2ab . Let us assume that a = 20 and b = 30.

What is a2 b2 c2 also known as?

The last equation, a2 + b2 = c2, is called the Pythagorean Theorem .

What formula is c2 a2 b2 2abcosC?

The law of cosines (often abbreviated LoC) states: For △ABC with sides a,b,c, the following relationships hold: c2=a2+b2−2abcosC a2=b2+c2−2abcosA b2=c2+a2−2cacosB This gives us a way to find the third side of a triangle, given two sides and the angle measure between them.

What theorem is often expressed as a2+b2 c2?

The Pythagorean theorem helps find the lengths of the sides of a right triangle. It states that a²+b²=c², where a and b are the sides around the right angle and c is the hypotenuse.

a^2 - b^2 Formula - Examples | A Square

The a² - b² formula is also known as "the difference of squares formula". The a square minus b square is used to find the difference between the two squares without actually calculating the squares.

It is one of the algebraic identities.
It is used to factorize the binomials of squares.

What is a^2-b^2 Formula?

The a² - b² formula is given as: a² - b² = (a - b) (a + b).

If you would like to verify this, you can just multiply (a - b) and (a + b) and see whether you get a² - b².

Verification of a² - b² Formula

Let us see the proof of a square minus b square formula. To verify that a² - b² = (a - b) (a + b) we need to prove LHS = RHS. Let us try to solve the equation:

a² - b² = (a - b) (a + b)

Multiply the binomials (a - b) and (a + b) we get

(a - b) (a + b)

=a (a + b) - b (a + b)

=a² + ab - ba - b²

=a² + 0 + b²

=a² - b²

Hence Verified

a² - b² = (a - b) (a + b)

You can understand the a² - b² formula geometrically using the following figure:

☛ Also Check:

(a-b)^2 Formula
(a+b)^2 Formula

Proof of a^2 - b^2 Formula

The proof that the value a² - b² is (a + b)(a - b). Let us consider the above figure. Take the two squares of sides a units and b units respectively. They can be arranged such that two rectangles are also formed as shown in the above figure.

One rectangle has a length of 'a' unit and a breadth of (a - b) units on the other side the second rectangle has a length of (a - b) and a breadth of 'b' units. Now add the areas of the two rectangles to obtain the resultant values. The respective areas of the two rectangles are (a - b) × a = a(a - b) , and (a - b) × b = b(a - b). The sum of the areas of rectangles is the actual obtained resultant expression i.e., a(a - b) + b(a - b) = (a - b)(a + b). Again re-arranging the individual rectangles and squares, we get: (a + b)(a − b) = a² − b².

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Examples on a^2-b^2 Formula

Let us solve some interesting problems using the a^2-b^2 formula.

Example 1: Using a² - b² formula find the value of 106² - 6².

Solution: To find: 100² - 6².

Let us assume that a = 100 and b = 6.

We will substitute these in the a² - b² formula.

a² - b² = (a - b) (a + b)

106²- 6² = (106 - 6) (106 + 6)

= (100) (112)

= 11200

Answer: 106² - 6² = 11200.

Example 2: Factorize the expression 25x² - 64.

Solution: To factorize: 25x² - 64.

We will use the a² - b² formula to factorize this.

We can write the given expression as

25x² - 64 = (5x)² - 8²

We will substitute a = 5x and b = 8 in the formula of a² - b².

a² - b² = (a - b) (a + b)

(5x)² - 8² = (5x - 8) (5x + 8)

Answer: 25x² - 64 = (5x - 8) (5x + 8)

Example 3: Simplify 10² - 5² using a² - b² formula

Solution: To find 10² - 5²

Let us assume a = 10 and b = 5

Using formula a² - b² = (a - b) (a + b)

10² - 5² = (10 - 5) (10 + 5)

= 10(10 +5) - 5(10 + 5)

= 10(15) - 5(15)

= 150-75 = 75

Answer: 10² - 5² = 75.

FAQs on a^2 - b^2 Formula

What is the Expansion of a² - b² Formula?

a² - b² formula is read as a square minus b square. Its expansion is expressed as a² - b² = (a - b) (a + b).

What is the a² - b² Formula in Algebra?

The a² - b² formula is also known as one of the important algebraic identities. It is read as a square - b square. a² - b² formula is expressed as a² - b² = (a - b) (a + b). It says, the difference of squares of two numbers is the product of their sum and the difference.

What is the Difference Between a square - b square and a - b Whole Square?

These two formulas are completely different:

a² - b² = (a - b) (a + b)
(a - b)2 = a² + b² - 2ab

How to Simplify Numbers Using the a² - b² Formula?

Let us understand the use of the a² - b² formula with the help of the following example.

Example: Find the value of 10² - 2² using the a² - b² formula.

To find: 10² - 2²

Let us assume that a = 10 and b = 2.

We will substitute these in the formula of a² - b².

a² - b² = (a - b) (a + b)

10²-2² = (10 - 2)(10 + 2)

= 10 (10 + 2) - 2 (10 + 2)

= 10(12) - 2(12)

=120 - 24 = 96

Answer: 10² - 2² = 96.

How To Use the a² - b² Formula Give Steps?

The following steps are followed while using a square - b square formula.

First, observe the pattern of the numbers and whether the numbers have ^2 as power or not.
Write down the formula of a² - b²
a² - b² = (a - b) (a + b)
Substitute the values of a and b in the a² - b² formula and simplify.

Is a Square Minus b Square Same as a Square Plus b Square?

No, these two have different formulas:

a² - b² = (a - b) (a + b)
a2 + b2 = (a + b)² - 2ab

a^2 - b^2 Formula - Examples | A Square - B Square Formula (2024)

What is a^2-b^2 Formula?

Verification of a² - b² Formula

Proof of a^2 - b^2 Formula

Examples on a^2-b^2 Formula

FAQs on a^2 - b^2 Formula

What is the Expansion of a² - b² Formula?

What is the a² - b² Formula in Algebra?

What is the Difference Between a square - b square and a - b Whole Square?

How to Simplify Numbers Using the a² - b² Formula?

How To Use the a² - b² Formula Give Steps?

Is a Square Minus b Square Same as a Square Plus b Square?

FAQs