Simplifying the Expression: (−5x2+5x−5)−(3x2+x)
This expression involves subtracting one polynomial from another. To simplify it, we'll follow these steps:
1. Distribute the Negative Sign:
Since we're subtracting the entire second polynomial, we need to distribute the negative sign to each term inside the parentheses.
(-5x<sup>2</sup> + 5x - 5) - (3x<sup>2</sup> + x) becomes
-5x<sup>2</sup> + 5x - 5 - 3x<sup>2</sup> - x
2. Combine Like Terms:
Now, we identify terms with the same variable and exponent and combine their coefficients:
-5x<sup>2</sup> - 3x<sup>2</sup> + 5x - x - 5
This simplifies to:
-8x<sup>2</sup> + 4x - 5
Therefore, the simplified form of the expression (−5x<sup>2</sup>+5x−5)−(3x<sup>2</sup>+x) is -8x<sup>2</sup> + 4x - 5.