%5E2-answer.jpeg "(x+y)^2 Answer")
Understanding (x+y)^2
The expression (x+y)^2 is a fundamental concept in algebra, often referred to as "squaring a binomial". It represents the product of the binomial (x+y) with itself.
Expanding the Expression
To find the answer, we need to expand the expression:
(x+y)^2 = (x+y)(x+y)
Using the distributive property (or FOIL method), we multiply each term in the first binomial by each term in the second binomial:
(x+y)(x+y) = x(x) + x(y) + y(x) + y(y)
Simplifying the terms:
x^2 + xy + xy + y^2
Combining like terms:
x^2 + 2xy + y^2
The Formula
This expansion leads to the widely used formula for squaring a binomial:
(x+y)^2 = x^2 + 2xy + y^2
This formula can be applied to any binomials, simply replacing 'x' and 'y' with the respective terms.
Applications
Understanding (x+y)^2 has numerous applications in various fields, including:
- Algebraic manipulation: This formula is crucial for simplifying and solving equations, especially in quadratic equations.
- Geometry: It plays a role in calculating areas of squares and rectangles.
- Calculus: It is used in differentiation and integration.
Conclusion
The expression (x+y)^2 holds significant importance in mathematics and its related disciplines. By understanding its expansion and formula, we gain a powerful tool for solving problems and exploring more complex concepts.