%5E2-formula.jpeg "(a*b)^2 Formula")
(a*b)^2 Formula: A Comprehensive Guide
The (a*b)^2 formula is a fundamental concept in algebra, and it is essential to understand its application and proof. In this article, we will delve into the details of the formula, its derivation, and examples to illustrate its usage.
What is the (a*b)^2 Formula?
The (a*b)^2 formula states that the square of the product of two numbers, a and b, is equal to the product of their squares:
(a*b)^2 = a^2 * b^2
This formula is a widely used identity in mathematics, particularly in algebra and geometry.
Derivation of the (a*b)^2 Formula
To derive the (a*b)^2 formula, let's start with the definition of the square of a number:
a^2 = a * a
Now, let's consider the product of a and b:
a * b
When we square this product, we get:
(a * b)^2 = (a * b) * (a * b)
Using the distributive property of multiplication over addition, we can expand the right-hand side of the equation as follows:
(a * b)^2 = a * a * b * b
Now, we can rearrange the terms to get:
(a * b)^2 = a^2 * b^2
This is the (a*b)^2 formula.
Examples of the (a*b)^2 Formula
Let's consider a few examples to illustrate the application of the (a*b)^2 formula:
Example 1
Find the value of (2*3)^2 using the formula.
(2*3)^2 = 2^2 * 3^2 (2*3)^2 = 4 * 9 (2*3)^2 = 36
Example 2
Simplify the expression (x*y)^2 using the formula.
(x*y)^2 = x^2 * y^2
Example 3
Find the value of (4*5)^2 using the formula.
(4*5)^2 = 4^2 * 5^2 (4*5)^2 = 16 * 25 (4*5)^2 = 400
Conclusion
In conclusion, the (a*b)^2 formula is a powerful tool in algebra that can be applied in various mathematical problems. By understanding its derivation and application, you can simplify complex expressions and solve equations with ease.
