Perform the following operation: (-8x^2 - 5x + 8) - (-6x^2 + 3x - 3)
Understand the Problem
The question requires us to perform the operation of subtracting one polynomial from another. We need to distribute the negative sign to the second polynomial, then combine like terms to simplify the expression.
Answer
$-2x^2 - 8x + 11$
Answer for screen readers
$-2x^2 - 8x + 11$
Steps to Solve
- Distribute the negative sign
Distribute the negative sign in the second polynomial to each term inside the parentheses.
$(-8x^2 - 5x + 8) - (-6x^2 + 3x - 3) = -8x^2 - 5x + 8 + 6x^2 - 3x + 3$
- Combine like terms
Group and combine like terms (terms with the same variable and exponent).
$(-8x^2 + 6x^2) + (-5x - 3x) + (8 + 3)$
- Simplify
Perform the addition and subtraction for each group of like terms.
$-2x^2 - 8x + 11$
$-2x^2 - 8x + 11$
More Information
The result is a simplified polynomial in standard form, which means the terms are arranged from the highest to the lowest degree.
Tips
A common mistake is not correctly distributing the negative sign to all terms in the second polynomial. For example forgetting to change $-3$ to $+3$.
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