(y^2-4y+9)-(3y^2-6y-9)=

2 min read Jun 17, 2024

Simplifying Algebraic Expressions: (y^2-4y+9)-(3y^2-6y-9)

This article will guide you through the process of simplifying the algebraic expression: (y^2-4y+9)-(3y^2-6y-9).

Understanding the Problem

The expression involves subtracting one trinomial (a polynomial with three terms) from another. To simplify it, we need to distribute the negative sign and then combine like terms.

Step-by-Step Solution

Distribute the negative sign: The negative sign in front of the second parenthesis means we multiply each term inside the parenthesis by -1. (y^2 - 4y + 9) + (-1 * 3y^2) + (-1 * -6y) + (-1 * -9)
Simplify the expression: This gives us: y^2 - 4y + 9 - 3y^2 + 6y + 9
Combine like terms: Group the terms with the same variable and exponent together: (y^2 - 3y^2) + (-4y + 6y) + (9 + 9)
Combine coefficients: -2y^2 + 2y + 18

Final Answer

The simplified form of the expression (y^2-4y+9)-(3y^2-6y-9) is -2y^2 + 2y + 18.

Key Points to Remember

Distribute: Always distribute the negative sign when subtracting polynomials.
Combine Like Terms: Combine terms with the same variable and exponent.
Order Matters: While the order of terms doesn't affect the final answer, it's often preferred to write the terms in descending order of their exponents.