(x-3)(x^2+3x+9) Answer

Jasonbradley

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Jun 17, 2024

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Expanding the Expression: (x-3)(x^2 + 3x + 9)

This expression represents the product of a binomial and a trinomial. We can expand it using the distributive property, also known as FOIL (First, Outer, Inner, Last).

Here's how to expand the expression:

1. Multiply the first terms of each expression: x * x² = x³

2. Multiply the outer terms: x * 3x = 3x²

3. Multiply the inner terms: -3 * x² = -3x²

4. Multiply the last terms: -3 * 9 = -27

Now, combine the terms:

x³ + 3x² - 3x² - 27

Simplifying the expression, we get:

x³ - 27

Therefore, the expanded form of (x-3)(x^2 + 3x + 9) is x³ - 27.

Understanding the pattern:

This expansion demonstrates a special pattern in algebra: the difference of cubes.

The expression (x³ - 27) can be factored as the difference of two cubes:

• x³ = (x)³
• 27 = (3)³

The general formula for the difference of cubes is:

a³ - b³ = (a - b)(a² + ab + b²)

In our example, a = x and b = 3.

Key takeaway:

Knowing how to expand and factor expressions like (x-3)(x^2 + 3x + 9) is essential for solving various algebraic problems and understanding mathematical patterns.