(x^2-9)(x+3)-(2x-7)(x-3)

Jasonbradley

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Jun 17, 2024

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Simplifying the Expression: (x^2-9)(x+3)-(2x-7)(x-3)

This article will guide you through the process of simplifying the given expression: (x^2-9)(x+3)-(2x-7)(x-3).

Understanding the Expression

The expression involves two multiplications and a subtraction. We will use the distributive property to expand these multiplications and then combine like terms to simplify.

Step-by-Step Simplification

1. Expand the first multiplication: (x^2-9)(x+3) = x^2(x+3) - 9(x+3) = x^3 + 3x^2 - 9x - 27

2. Expand the second multiplication: (2x-7)(x-3) = 2x(x-3) - 7(x-3) = 2x^2 - 6x - 7x + 21

3. Combine the expanded expressions: (x^3 + 3x^2 - 9x - 27) - (2x^2 - 6x - 7x + 21)

4. Distribute the negative sign: x^3 + 3x^2 - 9x - 27 - 2x^2 + 6x + 7x - 21

5. Combine like terms: x^3 + (3x^2 - 2x^2) + (-9x + 6x + 7x) + (-27 - 21)

6. Simplify: x^3 + x^2 + 4x - 48

Final Answer

Therefore, the simplified form of the expression (x^2-9)(x+3)-(2x-7)(x-3) is x^3 + x^2 + 4x - 48.