(9x3+2x2−5x+4)−(5x3−7x+4)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions: (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4)

This article will guide you through simplifying the algebraic expression: (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4).

Understanding the Process

To simplify this expression, we need to follow these steps:

1. Distribute the negative sign: The negative sign before the second set of parentheses means we multiply each term inside the parentheses by -1.
2. Combine like terms: We group together terms with the same variable and exponent.
3. Simplify: We perform the necessary arithmetic operations.

Step-by-Step Solution

1. Distribute the negative sign:

   (9x³ + 2x² - 5x + 4) -1(5x³ - 7x + 4)

   = 9x³ + 2x² - 5x + 4 - 5x³ + 7x - 4

2. Combine like terms:

   9x³ - 5x³ + 2x² + -5x + 7x + 4 - 4

3. Simplify:

   4x³ + 2x² + 2x

Final Result

Therefore, the simplified expression for (9x³ + 2x² - 5x + 4) - (5x³ - 7x + 4) is 4x³ + 2x² + 2x.