Simplifying Algebraic Expressions: (x^2 + 2x  5)  (3x^2  4x + 7)
This article will guide you through the process of simplifying the algebraic expression: (x^2 + 2x  5)  (3x^2  4x + 7).
Understanding the Problem
We are asked to subtract the expression (3x^2  4x + 7) from (x^2 + 2x  5). This involves applying the rules of algebra to combine like terms and arrive at a simplified expression.
StepbyStep Solution

Distribute the negative sign: The minus sign in front of the second parenthesis means we multiply each term inside by 1. (x^2 + 2x  5) 1(3x^2  4x + 7)

Simplify the expression: x^2 + 2x  5  3x^2 + 4x  7

Combine like terms: Group together terms with the same variable and exponent. (x^2  3x^2) + (2x + 4x) + (5  7)

Simplify: 2x^2 + 6x  12
The Solution
Therefore, the simplified expression for (x^2 + 2x  5)  (3x^2  4x + 7) is 2x^2 + 6x  12.
Key Points
 Distributing the negative sign: Remember to change the signs of all terms within the parentheses when subtracting expressions.
 Combining like terms: This is essential for simplifying algebraic expressions.
 Order of operations: Follow the order of operations (PEMDAS/BODMAS) to ensure accurate simplification.