2-formula.jpeg "(x2+y2)2 Formula")
Understanding the (x² + y²)² Formula
The formula (x² + y²)² is a common algebraic expression used in various mathematical contexts. It represents the square of the sum of squares of two variables, x and y. This formula can be expanded using the distributive property of multiplication:
Expanding the Formula
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Step 1: Write the expression as the product of two identical binomials: (x² + y²)² = (x² + y²)(x² + y²)
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Step 2: Apply the distributive property, multiplying each term in the first binomial by each term in the second binomial: (x² + y²)(x² + y²) = x² * x² + x² * y² + y² * x² + y² * y²
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Step 3: Simplify by combining like terms: x⁴ + x²y² + x²y² + y⁴ = x⁴ + 2x²y² + y⁴
Applications of the Formula
The formula (x² + y²)² is often used in:
- Geometry: It helps calculate the area of a square with sides of length (x² + y²).
- Trigonometry: It appears in trigonometric identities, such as the Pythagorean identity (sin²θ + cos²θ = 1).
- Algebra: It is used in solving equations and simplifying expressions involving squared terms.
Example
Let's say x = 2 and y = 3. Using the formula (x² + y²)², we can calculate:
(2² + 3²)² = (4 + 9)² = 13² = 169
Conclusion
The formula (x² + y²)² is a fundamental algebraic expression that finds applications in various mathematical fields. By understanding how to expand and apply this formula, you can tackle complex mathematical problems involving squares and sums.