(y^2-4y+9)-(3y^2-6y-9) Find The Difference

Jasonbradley

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Jun 17, 2024

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Finding the Difference: (y^2 - 4y + 9) - (3y^2 - 6y - 9)

This problem asks us to find the difference between two polynomials. Here's how to solve it step-by-step:

1. Distribute the negative sign: The minus sign in front of the second set of parentheses means we need to multiply each term inside the parentheses by -1.

   This gives us: (y^2 - 4y + 9) + (-1 * 3y^2) + (-1 * -6y) + (-1 * -9)

2. Simplify: Now, simplify the expression by multiplying the -1:

   y^2 - 4y + 9 - 3y^2 + 6y + 9

3. Combine like terms: Combine the terms with the same variable and exponent:

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

4. Final Result: Add the coefficients of the like terms:

   -2y^2 + 2y + 18

Therefore, the difference between the two polynomials (y^2 - 4y + 9) and (3y^2 - 6y - 9) is -2y^2 + 2y + 18.