To simplify the given expression [tex]\( -\left(-5z^2 + z - 3\right) \)[/tex], we need to distribute the negative sign through the parentheses. This involves changing the sign of each term inside the parentheses. Here's the step-by-step process:
1. Start with the expression:
[tex]\[
-\left(-5z^2 + z - 3\right)
\][/tex]
2. Distribute the negative sign to each term inside the parentheses. Essentially, we are multiplying each term by [tex]\(-1\)[/tex], which changes the sign of each term:
[tex]\[
-(-5z^2) + (-z) + 3
\][/tex]
3. Simplify each term individually:
- The term [tex]\(-(-5z^2)\)[/tex] becomes [tex]\(5z^2\)[/tex] because multiplying [tex]\(-1\)[/tex] by [tex]\(-5z^2\)[/tex] results in a positive [tex]\(5z^2\)[/tex].
- The term [tex]\(-z\)[/tex] becomes [tex]\(-z\)[/tex] because multiplying [tex]\(z\)[/tex] by [tex]\(-1\)[/tex] results in [tex]\(-z\)[/tex].
- The term [tex]\(3\)[/tex] remains [tex]\(3\)[/tex] since multiplying [tex]\(3\)[/tex] by [tex]\(-1\)[/tex] and then by [tex]\(-1\)[/tex] doesn't change it.
4. Combine these simplified terms into one expression:
[tex]\[
5z^2 - z + 3
\][/tex]
Therefore, the simplified form of the expression [tex]\( -\left(-5z^2 + z - 3\right) \)[/tex] is:
[tex]\[
5z^2 - z + 3
\][/tex]
