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Difference of Two Squares Formula
The formula (a+b)(a-b) is known as the Difference of Two Squares Formula. It is a fundamental concept in algebra and is widely used in various mathematical operations.
The Formula
The Difference of Two Squares Formula is stated as:
(a+b)(a-b) = a^2 - b^2
where a and b are any two numbers.
Proof
To prove the formula, let's expand the left-hand side of the equation:
(a+b)(a-b) = a(a-b) + b(a-b)
= a^2 - ab + ab - b^2
= a^2 - b^2
As we can see, the expansion of the formula results in the right-hand side of the equation, which is a^2 - b^2.
Examples
Let's consider a few examples to illustrate the application of the Difference of Two Squares Formula:
Example 1
Find the value of (x+3)(x-3).
Using the formula, we get:
(x+3)(x-3) = x^2 - 3^2
= x^2 - 9
Example 2
Find the value of (2y+5)(2y-5).
Using the formula, we get:
(2y+5)(2y-5) = (2y)^2 - 5^2
= 4y^2 - 25
Importance
The Difference of Two Squares Formula has numerous applications in various branches of mathematics, including:
- Algebra: It is used to simplify algebraic expressions and solve equations.
- Geometry: It is used to find the areas and volumes of various geometric shapes.
- Trigonometry: It is used to simplify trigonometric identities and prove trigonometric formulas.
In conclusion, the Difference of Two Squares Formula is a powerful tool in algebra and has a wide range of applications in various mathematical disciplines.
