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(x+5)2 Answer

3 min read Jun 17, 2024
(x+5)2 Answer

Understanding (x + 5)²

The expression (x + 5)² represents the square of the binomial (x + 5). This means we are multiplying the binomial by itself:

(x + 5)² = (x + 5)(x + 5)

To expand this expression, we can use the FOIL method (First, Outer, Inner, Last) or the distributive property.

Expanding using FOIL Method:

  • First: x * x = x²
  • Outer: x * 5 = 5x
  • Inner: 5 * x = 5x
  • Last: 5 * 5 = 25

Combining the terms: x² + 5x + 5x + 25 = x² + 10x + 25

Expanding using Distributive Property:

  1. Distribute the first term: x(x + 5) = x² + 5x
  2. Distribute the second term: 5(x + 5) = 5x + 25
  3. Combine the terms: x² + 5x + 5x + 25 = x² + 10x + 25

Therefore, the expanded form of (x + 5)² is x² + 10x + 25.

Key Points:

  • This expression represents a perfect square trinomial, a special type of trinomial where the first and last terms are perfect squares and the middle term is twice the product of the square roots of the first and last terms.
  • Understanding the expansion of this expression is crucial for solving equations, simplifying algebraic expressions, and working with quadratic functions.

Examples:

  • Evaluating for a specific value: If x = 2, then (x + 5)² = (2 + 5)² = 7² = 49.
  • Simplifying expressions: The expression 2(x + 5)² can be simplified as 2(x² + 10x + 25) = 2x² + 20x + 50.
  • Solving equations: An equation like (x + 5)² = 16 can be solved by taking the square root of both sides and then solving for x.

By understanding the expansion and properties of (x + 5)², you can manipulate and solve various mathematical problems.

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