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The Expansion of (x+y)^2
In algebra, the expansion of (x+y)^2 is a fundamental concept that is widely used in various mathematical operations. In this article, we will explore the answer to (x+y)^2 and its application in different mathematical problems.
The Answer to (x+y)^2
The expansion of (x+y)^2 can be obtained by using the distributive property of multiplication over addition, which states that:
(x+y)^2 = (x+y)(x+y)
By multiplying the two binomials, we get:
(x+y)(x+y) = x^2 + xy + xy + y^2
Combining like terms, we get:
(x+y)^2 = x^2 + 2xy + y^2
Therefore, the answer to (x+y)^2 is x^2 + 2xy + y^2.
Applications of (x+y)^2
The expansion of (x+y)^2 has numerous applications in various mathematical problems, including:
Algebraic Expressions
The expansion of (x+y)^2 is used to simplify algebraic expressions, such as:
(2x + 3y)^2 = (2x)^2 + 2(2x)(3y) + (3y)^2 = 4x^2 + 12xy + 9y^2
Geometry
In geometry, the expansion of (x+y)^2 is used to find the area of a square, rectangle, and other quadrilaterals.
Trigonometry
The expansion of (x+y)^2 is used in trigonometric identities, such as:
sin(a+b) = sin(a)cos(b) + cos(a)sin(b)
Calculus
In calculus, the expansion of (x+y)^2 is used to find the derivative and integral of functions.
Conclusion
In conclusion, the expansion of (x+y)^2 is a fundamental concept in algebra that has numerous applications in various mathematical problems. The answer to (x+y)^2 is x^2 + 2xy + y^2, which is used to simplify algebraic expressions, find the area of quadrilaterals, and apply to trigonometric identities and calculus.
