(a2−3ab+2b2)+(−4a2+5ab−b2)

less than a minute read Jun 16, 2024

Simplifying Algebraic Expressions: (a²−3ab+2b²)+(−4a²+5ab−b²)

In algebra, simplifying expressions often involves combining like terms. This means grouping terms with the same variables and exponents. Let's break down the simplification of the following expression:

(a²−3ab+2b²)+(−4a²+5ab−b²)

Step 1: Remove the Parentheses

Since we are adding the two expressions, the parentheses don't affect the order of operations. We can simply remove them:

a²−3ab+2b²−4a²+5ab−b²

Step 2: Identify Like Terms

a² terms: a², -4a²
ab terms: -3ab, 5ab
b² terms: 2b², -b²

Step 3: Combine Like Terms

Now, we combine the coefficients of the like terms:

a² terms: a² - 4a² = -3a²
ab terms: -3ab + 5ab = 2ab
b² terms: 2b² - b² = b²

Final Result

Therefore, the simplified expression is:

-3a² + 2ab + b²