%5E3-formula-class-10.jpeg "(x-y)^3 Formula Class 10")
The (x-y)^3 Formula: A Comprehensive Guide for Class 10 Students
The (x-y)^3 formula is an essential concept in algebra that is commonly used to solve various mathematical problems. In this article, we will delve into the world of algebra and explore the (x-y)^3 formula, its expansion, and examples to help Class 10 students understand this concept better.
What is the (x-y)^3 Formula?
The (x-y)^3 formula is a mathematical expression that represents the cube of the difference between two variables, x and y. It can be written as:
(x-y)^3 = x^3 - 3x^2y + 3xy^2 - y^3
This formula is used to find the cube of the difference between two variables, which is a fundamental concept in algebra.
Expansion of the (x-y)^3 Formula
To understand the (x-y)^3 formula better, let's expand it step by step:
(x-y)^3 = (x-y) × (x-y) × (x-y)
= (x^2 - 2xy + y^2) × (x - y)
= x^3 - x^2y - 2x^2y + 2xy^2 + xy^2 - y^3
= x^3 - 3x^2y + 3xy^2 - y^3
Examples to Illustrate the (x-y)^3 Formula
Let's consider a few examples to understand how to apply the (x-y)^3 formula:
Example 1:
Find the value of (2-3)^3 using the formula.
(2-3)^3 = 2^3 - 3(2^2)3 + 3(2)3^2 - 3^3
= 8 - 18 + 18 - 27
= -19
Example 2:
Find the value of (x-2)^3 when x = 4.
(x-2)^3 = x^3 - 3x^2(2) + 3x(2)^2 - 2^3
= 4^3 - 3(4^2)2 + 3(4)2^2 - 2^3
= 64 - 96 + 48 - 8
= 8
Conclusion
In conclusion, the (x-y)^3 formula is a powerful tool in algebra that helps in solving various mathematical problems. By understanding the expansion of the formula and practicing examples, Class 10 students can master this concept and apply it to solve complex problems. Remember to use the formula correctly and practice regularly to become proficient in algebra.
