-(m%5E2%2B3m-6)%2B(m%5E2-2m%2B4).jpeg "(m+2) (m^2+3m-6)+(m^2-2m+4)")
Simplifying Algebraic Expressions: A Step-by-Step Guide
This article will guide you through the process of simplifying the algebraic expression (m + 2)(m² + 3m - 6) + (m² - 2m + 4).
Step 1: Expand the Product
We begin by expanding the product of the first two terms using the distributive property (or FOIL method).
- (m + 2)(m² + 3m - 6) = m(m² + 3m - 6) + 2(m² + 3m - 6)
Expanding this further gives:
- m³ + 3m² - 6m + 2m² + 6m - 12
Step 2: Combine Like Terms
Combining the like terms in the expanded expression:
- m³ + 3m² + 2m² - 6m + 6m - 12 = m³ + 5m² - 12
Step 3: Combine with the Remaining Term
Now, add the remaining term to the simplified expression:
- (m³ + 5m² - 12) + (m² - 2m + 4)
Combine the like terms again:
- m³ + 5m² + m² - 2m - 12 + 4 = m³ + 6m² - 2m - 8
Final Result
Therefore, the simplified form of the expression (m + 2)(m² + 3m - 6) + (m² - 2m + 4) is m³ + 6m² - 2m - 8.
Key Points
- Distributive Property: This property is essential for expanding expressions involving multiplication.
- Combining Like Terms: Simplifying expressions often involves combining terms with the same variable and exponent.
- Order of Operations: Remember to follow the order of operations (PEMDAS/BODMAS) when simplifying algebraic expressions.
By following these steps, you can successfully simplify algebraic expressions like this one.