If `A=5x^(3)-11`,
`B=9x^(3)-2x^(2)+7`, and
`C=x^(2)+9`, then find
`A+(B+C)`.

Answer

To solve the problem, we need to find the expression \( A + (B + C) \) where:

- \( A = 5x^3 - 11 \)
- \( B = 9x^3 - 2x^2 + 7 \)
- \( C = x^2 + 9 \)

Let's break this down step by step.

### Step 1: Calculate \( B + C \)

We start by adding \( B \) and \( C \):

\[ B + C = (9x^3 - 2x^2 + 7) + (x^2 + 9) \]

Now, we combine like terms:

- The \( x^3 \) term: \( 9x^3 \)
- The \( x^2 \) terms: \( -2x^2 + x^2 = -x^2 \)
- The constant terms: \( 7 + 9 = 16 \)

So,

\[ B + C = 9x^3 - x^2 + 16 \]

### Step 2: Calculate \( A + (B + C) \)

Now we add \( A \) to the result from Step 1:

\[ A + (B + C) = (5x^3 - 11) + (9x^3 - x^2 + 16) \]

Again, we combine like terms:

- The \( x^3 \) terms: \( 5x^3 + 9x^3 = 14x^3 \)
- The \( x^2 \) term: \( -x^2 \)
- The constant terms: \( -11 + 16 = 5 \)

So,

\[ A + (B + C) = 14x^3 - x^2 + 5 \]

### Final Answer:

Thus, the final result is:

\[ A + (B + C) = 14x^3 - x^2 + 5 \]

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