%5E2-expand-and-simplify.jpeg "(x+y)^2 Expand And Simplify")
Expanding and Simplifying (x + y)^2
The expression (x + y)^2 is a common algebraic expression that appears in various mathematical contexts. It represents the square of the sum of two variables, x and y. Expanding and simplifying this expression is a fundamental skill in algebra.
Understanding the Concept
(x + y)^2 essentially means multiplying the binomial (x + y) by itself:
(x + y)^2 = (x + y)(x + y)
To expand this expression, we can use the distributive property:
- Multiply the first term of the first binomial by each term of the second binomial:
- x * x = x^2
- x * y = xy
- Multiply the second term of the first binomial by each term of the second binomial:
- y * x = xy
- y * y = y^2
Combining the results, we get:
(x + y)^2 = x^2 + xy + xy + y^2
Simplifying the Expression
Notice that we have two identical terms, xy, in the expanded form. Combining these terms, we get the simplified expression:
(x + y)^2 = x^2 + 2xy + y^2
Key Points to Remember
- The expanded form of (x + y)^2 is x^2 + 2xy + y^2.
- This expression represents the square of the first term (x^2), twice the product of the two terms (2xy), and the square of the second term (y^2).
- This formula can be used to expand and simplify various algebraic expressions involving squared binomials.
Example
Let's say we want to expand and simplify the expression (2a + 3b)^2. Applying the formula:
(2a + 3b)^2 = (2a)^2 + 2(2a)(3b) + (3b)^2
Simplifying further:
(2a + 3b)^2 = 4a^2 + 12ab + 9b^2
By understanding and applying the formula for expanding (x + y)^2, we can effectively manipulate and simplify algebraic expressions, paving the way for solving more complex equations and tackling higher-level mathematics.