(-4a+b-2c)-(3a+2b-c)

Jasonbradley

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Jun 16, 2024

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Simplifying the Expression: (-4a + b - 2c) - (3a + 2b - c)

This article will guide you through the process of simplifying the expression (-4a + b - 2c) - (3a + 2b - c).

Understanding the Concept

The expression involves subtracting two trinomials. Trinomials are algebraic expressions with three terms, each containing a variable, a coefficient, and sometimes a constant. To simplify the expression, we need to apply the distributive property and combine like terms.

Step-by-Step Solution

1. Distribute the negative sign:

   • Remember that subtracting an expression is the same as adding its negative counterpart. Therefore, we can rewrite the expression as: (-4a + b - 2c) + (-1)(3a + 2b - c)
   • Now, multiply the negative sign with each term inside the second parenthesis: -4a + b - 2c - 3a - 2b + c

2. Combine like terms:

   • Identify terms with the same variable and exponent. For example, -4a and -3a are like terms.
   • Combine the coefficients of like terms: (-4a - 3a) + (b - 2b) + (-2c + c)

3. Simplify the expression:

   • -7a - b - c

Final Answer

Therefore, the simplified expression is -7a - b - c.

Key Points to Remember

• Always distribute the negative sign carefully.
• Combine like terms only.
• Remember that the order of terms in the final answer doesn't affect the value of the expression.