To evaluate the expression \(4(a^2 + 2b) - 2b\) when \(a = 2\) and \(b = -2\), let's proceed step-by-step.
1. Substitute the values of \(a\) and \(b\):
- \(a = 2\)
- \(b = -2\)
2. Evaluate \(a^2\):
- \(a^2 = 2^2 = 4\)
- Thus, we have \(a^2 = 4\).
3. Evaluate \(2b\):
- \(2b = 2 \times (-2) = -4\)
- Thus, we have \(2b = -4\).
4. Evaluate the expression inside the parentheses \(a^2 + 2b\):
- \(a^2 + 2b = 4 + (-4) = 4 - 4 = 0\)
- Thus, we have \(a^2 + 2b = 0\).
5. Multiply the result by 4:
- \(4(a^2 + 2b) = 4 \times 0 = 0\)
- Thus, we have \(4(a^2 + 2b) = 0\).
6. Evaluate \(-2b\):
- \(-2b = -2 \times (-2) = 4\)
- Thus, we have \(-2b = 4\).
7. Subtract \(2b\) from the result of the previous step:
- [tex]\[4(a^2 + 2b) - 2b = 0 - 4 = 4\][/tex]
Thus, the evaluated expression \(4(a^2 + 2b) - 2b\) when \(a = 2\) and \(b = -2\) is:
[tex]\[
\boxed{4}
\][/tex]
