RaizaSequijor
Answered

Perform the indicated operations.

[tex]\[
\begin{array}{l}
\left(3b^2 + 2b - 2\right) - \left(b^2 - 3b + 7\right) \\
\left(5 - 2p^4 + 7p^2\right) - \left(4p^2 - 7 - p^4\right)
\end{array}
\][/tex]



Answer :

GinnyAnswer
Sure, let's perform the indicated operations step-by-step.

### 1. Perform the operation:
[tex]\[ (3b^2 + 2b - 2) - (b^2 - 3b + 7) \][/tex]

First, distribute the negative sign across the second polynomial:
[tex]\[ (3b^2 + 2b - 2) - b^2 + 3b - 7 \][/tex]

Next, combine like terms:

- Combine [tex]\(b^2\)[/tex] terms:
[tex]\[ 3b^2 - b^2 = 2b^2 \][/tex]

- Combine [tex]\(b\)[/tex] terms:
[tex]\[ 2b + 3b = 5b \][/tex]

- Combine constant terms:
[tex]\[ -2 - 7 = -9 \][/tex]

Thus, the result is:
[tex]\[ 2b^2 + 5b - 9 \][/tex]

### 2. Perform the operation:
[tex]\[ (5 - 2p^4 + 7p^2) - (4p^2 - 7 - p^4) \][/tex]

First, distribute the negative sign across the second polynomial:
[tex]\[ 5 - 2p^4 + 7p^2 - 4p^2 + 7 + p^4 \][/tex]

Next, combine like terms:

- Combine [tex]\(p^4\)[/tex] terms:
[tex]\[ -2p^4 + p^4 = -p^4 \][/tex]

- Combine [tex]\(p^2\)[/tex] terms:
[tex]\[ 7p^2 - 4p^2 = 3p^2 \][/tex]

- Combine constant terms:
[tex]\[ 5 + 7 = 12 \][/tex]

Thus, the result is:
[tex]\[ 12 - p^4 + 3p^2 \][/tex]

Therefore, the final results from the given operations are:
[tex]\[ \begin{aligned} &\left(3b^2 + 2b - 2\right) - \left(b^2 - 3b + 7\right) = 2b^2 + 5b - 9, \\ &\left(5 - 2p^4 + 7p^2\right) - \left(4p^2 - 7 - p^4\right) = 12 - p^4 + 3p^2. \end{aligned} \][/tex]

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