(-4a^2b+3ab^2+ab)-(2a^2b-3ab^2-5ab)

Jasonbradley

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Jun 16, 2024

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Simplifying Algebraic Expressions

This article will guide you through simplifying the algebraic expression: (-4a²b + 3ab² + ab) - (2a²b - 3ab² - 5ab)

Understanding the Expression

The expression involves several terms with variables a and b, and exponents.

• Terms: Each part of the expression separated by + or - signs is a term. For example, -4a²b is a term.
• Coefficients: The numerical part of a term is the coefficient. For example, in -4a²b, the coefficient is -4.
• Variables: The letters in the expression represent variables. Here, we have variables a and b.
• Exponents: The small numbers written above the variables indicate exponents. For example, in -4a²b, the exponent of a is 2.

Simplifying the Expression

To simplify the expression, we'll follow these steps:

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we multiply each term inside the parentheses by -1. (-4a²b + 3ab² + ab) + (-1)(2a²b) + (-1)(-3ab²) + (-1)(-5ab)

2. Combine like terms: Like terms have the same variables raised to the same powers. We can combine the coefficients of like terms. (-4a²b - 2a²b) + (3ab² + 3ab²) + (ab + 5ab)

3. Simplify: Combine the coefficients of each group of like terms. -6a²b + 6ab² + 6ab

Final Result

The simplified form of the expression is -6a²b + 6ab² + 6ab.