Lane Weber
02/05/2023 · High School
Subtract: \( \left(4 b^{2}-8 b+11\right)-\left(-2 b^{2}-4 b+5\right) \) \( 2 b^{2}-12 b+16 \) \( 2 b^{2}-12 b+6 \) \( 6 b^{2}-12 b+6 \) \( 6 b^{2}-4 b+6 \)
UpStudy ThothAI Solution
Tutor-Verified Answer
Step-by-step Solution
To solve the expression \( \left(4 b^{2}-8 b+11\right)-\left(-2 b^{2}-4 b+5\right) \), we first distribute the negative sign across the second expression:
\[
\left(4 b^{2}-8 b+11\right) - \left(-2 b^{2}-4 b+5\right) = \left(4 b^{2}-8 b+11\right) + \left(2 b^{2}+4 b-5\right)
\]
Now, we can combine the like terms:
1. Combine the \( b^2 \) terms:
\[
4 b^{2} + 2 b^{2} = 6 b^{2}
\]
2. Combine the \( b \) terms:
\[
-8 b + 4 b = -4 b
\]
3. Combine the constant terms:
\[
11 - 5 = 6
\]
Putting it all together, we have:
\[
6 b^{2} - 4 b + 6
\]
Thus, the result of the subtraction is:
\[
\boxed{6 b^{2}-4 b+6}
\]
Quick Answer
The result of the subtraction is \( 6 b^{2}-4 b+6 \).
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