(x+3)(x-3) Standard Form

Jasonbradley

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Jun 16, 2024

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Understanding the Standard Form of (x+3)(x-3)

In algebra, the standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants. To understand the standard form of (x+3)(x-3), we need to expand the expression using the distributive property or the FOIL method.

Expanding (x+3)(x-3)

1. Using the Distributive Property:

• We distribute each term in the first set of parentheses to the second set of parentheses:
  • x(x-3) + 3(x-3)
• Then, we simplify by multiplying:
  • x² - 3x + 3x - 9

2. Using the FOIL Method:

• FOIL stands for First, Outer, Inner, Last. We multiply each pair of terms as follows:
  • First: x * x = x²
  • Outer: x * -3 = -3x
  • Inner: 3 * x = 3x
  • Last: 3 * -3 = -9
• We then combine the like terms:
  • x² - 3x + 3x - 9

The Standard Form

After simplifying, we get: x² - 9

This is the standard form of the quadratic expression (x+3)(x-3). Notice that the b term (the coefficient of x) is 0 in this case.

Significance of the Standard Form

The standard form of a quadratic expression is crucial because it:

• Simplifies the expression: It provides a concise and organized way to represent the equation.
• Facilitates calculations: It allows us to easily identify the coefficients (a, b, and c) which are necessary for solving the equation or finding its vertex.
• Enables comparisons: It allows us to compare different quadratic expressions and identify their key features.

In the case of (x+3)(x-3), the standard form x² - 9 reveals that the expression represents a parabola with a vertex at (0, -9) and symmetric about the y-axis. This knowledge helps us understand the graph of the equation and its properties.