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

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Jul 03, 2024

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(a-b)² = a² - 2ab + b²: Examples and Explanations

The concept of (a-b)² = a² - 2ab + b² is a fundamental algebraic identity that has numerous applications in mathematics and other fields. In this article, we will delve into the explanations and examples of this important formula.

What is the Formula?

The formula (a-b)² = a² - 2ab + b² is a quadratic expression that represents the expansion of the expression (a-b) squared. This formula is commonly used in algebra, geometry, trigonometry, and other areas of mathematics.

How Does it Work?

To understand how the formula works, let's break it down:

• (a-b) is the binomial expression being squared.
• a² represents the square of the first term a.
• -2ab represents the product of the two terms a and b, with a negative sign.
• b² represents the square of the second term b.

When we multiply (a-b) by itself, we get:

(a-b)(a-b) = a² - ab - ab + b²

Combining like terms, we get:

(a-b)² = a² - 2ab + b²

Examples

Here are a few examples to illustrate the application of the formula:

Example 1

Find the value of (3-2)² using the formula.

Solution:

(3-2)² = 3² - 2(3)(2) + 2² = 9 - 12 + 4 = 1

Therefore, (3-2)² = 1.

Example 2

Simplify the expression (x-5)².

Solution:

Using the formula, we get:

(x-5)² = x² - 2(x)(5) + 5² = x² - 10x + 25

Therefore, (x-5)² = x² - 10x + 25.

Example 3

Find the value of (a-b)² when a = 4 and b = 3.

Solution:

Substituting the values in the formula, we get:

(4-3)² = 4² - 2(4)(3) + 3² = 16 - 24 + 9 = 1

Therefore, (4-3)² = 1.

Conclusion

The formula (a-b)² = a² - 2ab + b² is a powerful tool in algebra and other areas of mathematics. It allows us to simplify complex expressions and solve problems easily. By understanding and applying this formula, you can improve your math skills and tackle a wide range of problems.