Simplifying the Expression: (8x² + 2x – 6) – (5x² – 3x + 2)
This article will guide you through the steps to simplify the given expression: (8x² + 2x – 6) – (5x² – 3x + 2).
Understanding the Problem
The expression involves subtracting two polynomials. To simplify it, we need to apply the distributive property and combine like terms.
Steps to Simplify

Distribute the negative sign: The minus sign in front of the second polynomial implies that we are subtracting each term within the parentheses.
(8x² + 2x – 6) + (1)(5x² – 3x + 2)

Multiply the second polynomial by 1:
(8x² + 2x – 6) + (5x² + 3x  2)

Combine like terms: Group the terms with the same variable and exponent.
(8x²  5x²) + (2x + 3x) + (6  2)

Simplify: Perform the operations within each group.
3x² + 5x  8
Solution
The simplified form of the expression (8x² + 2x – 6) – (5x² – 3x + 2) is 3x² + 5x  8.