(x+y)^2 Formula Class 9

4 min read Jun 17, 2024
(x+y)^2 Formula Class 9

Understanding the (x + y)² Formula in Class 9

The (x + y)² formula is a fundamental concept in algebra that plays a crucial role in simplifying expressions and solving equations. It's essential for students in Class 9 to grasp this formula thoroughly to excel in their math studies.

The Formula and Its Derivation

The (x + y)² formula states that:

(x + y)² = x² + 2xy + y²

This formula can be derived by expanding the expression (x + y)²:

(x + y)² = (x + y)(x + y)

Using the distributive property, we multiply each term in the first bracket by each term in the second bracket:

(x + y)(x + y) = x(x + y) + y(x + y)

Expanding further:

x(x + y) + y(x + y) = x² + xy + xy + y²

Combining like terms:

x² + xy + xy + y² = x² + 2xy + y²

Applying the Formula

The (x + y)² formula can be applied in various situations, including:

  • Simplifying algebraic expressions: When encountering expressions like (a + b)², we can directly substitute the formula to get a² + 2ab + b² and simplify further.
  • Solving equations: In equations containing squared terms, we can use the formula to rewrite them in a simpler form. For example, if we have the equation (x + 3)² = 16, we can apply the formula to get x² + 6x + 9 = 16 and solve for x.
  • Factoring expressions: The formula can be used in reverse to factor expressions of the form x² + 2xy + y² as (x + y)².

Examples

Let's look at some examples to illustrate the application of the (x + y)² formula:

Example 1:

Simplify the expression (2a + 3b)².

Applying the formula:

(2a + 3b)² = (2a)² + 2(2a)(3b) + (3b)²

Expanding and simplifying:

= 4a² + 12ab + 9b²

Example 2:

Solve the equation (x + 5)² = 25.

Using the formula:

x² + 10x + 25 = 25

Subtracting 25 from both sides:

x² + 10x = 0

Factoring out x:

x(x + 10) = 0

Therefore, x = 0 or x = -10

Conclusion

The (x + y)² formula is a powerful tool in algebra that helps simplify expressions, solve equations, and factor expressions. Mastering this formula is crucial for success in Class 9 math and beyond. Through practice and application, students can gain a deep understanding of this fundamental concept and its various uses.

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