(11b^2-4b+7)-(b^2+8b-9)

3 min read Jun 16, 2024

Simplifying Algebraic Expressions: (11b^2 - 4b + 7) - (b^2 + 8b - 9)

This article will guide you through simplifying the expression (11b^2 - 4b + 7) - (b^2 + 8b - 9). Understanding how to simplify expressions like this is crucial for various mathematical tasks, including solving equations and working with polynomials.

Understanding the Problem

The problem presents two sets of terms enclosed in parentheses, with a subtraction sign between them. The goal is to combine like terms and remove the parentheses to arrive at a simplified expression.

Step-by-Step Solution

Distribute the negative sign:
- Since we're subtracting the entire second set of terms, we need to distribute the negative sign to each term within the parentheses. This means changing the sign of each term inside the second set of parentheses.
(11b^2 - 4b + 7) - (b^2 + 8b - 9) = 11b^2 - 4b + 7 - b^2 - 8b + 9
Combine like terms:
- Identify terms with the same variable and exponent. Combine their coefficients.
- b^2 terms: 11b^2 - b^2 = 10b^2
- b terms: -4b - 8b = -12b
- Constant terms: 7 + 9 = 16
Write the simplified expression:
- Combine the simplified terms: 10b^2 - 12b + 16

Final Answer

The simplified form of the expression (11b^2 - 4b + 7) - (b^2 + 8b - 9) is 10b^2 - 12b + 16.

Key Points to Remember

Distribute the negative sign: This is crucial when dealing with subtracting a group of terms enclosed in parentheses.
Identify like terms: Combine terms with the same variable and exponent.
Simplify by combining coefficients: Add or subtract the coefficients of like terms.

By following these steps, you can successfully simplify algebraic expressions involving parentheses and subtraction.