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(x+9)^2 In Standard Form

2 min read Jun 17, 2024
(x+9)^2 In Standard Form

Expanding (x + 9)² to Standard Form

The expression (x + 9)² represents the square of the binomial (x + 9). To rewrite it in standard form, we need to expand it using the distributive property or the FOIL method.

Understanding the Process

1. Distribute: We can use the distributive property twice:

  • (x + 9)² = (x + 9)(x + 9)
  • = x(x + 9) + 9(x + 9)

2. Simplify: Now, distribute each term:

  • = x² + 9x + 9x + 81

3. Combine Like Terms: Combine the terms with 'x':

  • = x² + 18x + 81

Standard Form

The standard form of a quadratic expression is ax² + bx + c, where a, b, and c are constants.

Therefore, the standard form of (x + 9)² is x² + 18x + 81.

Key Points

  • Squaring a binomial: When you square a binomial, you're essentially multiplying it by itself.
  • Distributive property: This property allows us to multiply each term within a set of parentheses by the term outside.
  • FOIL method: This acronym (First, Outer, Inner, Last) helps remember the order of multiplication when expanding two binomials.

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