If `p(y)=y^(3)-5y^(2)+5y+10` , then find p(2) +p(-2).

Answer

To solve the problem, we need to find the values of \( p(2) \) and \( p(-2) \) using the polynomial \( p(y) = y^3 - 5y^2 + 5y + 10 \), and then add these two values together.

### Step 1: Calculate \( p(2) \)

Substituting \( y = 2 \) into the polynomial:

\[ p(2) = (2)^3 - 5(2)^2 + 5(2) + 10 \]

Calculating each term:

\[ = 8 - 5(4) + 10 + 10 \]
\[ = 8 - 20 + 10 + 10 \]
\[ = 8 - 20 + 20 \]
\[ = 8 \]

So, \( p(2) = 8 \).

### Step 2: Calculate \( p(-2) \)

Now substituting \( y = -2 \) into the polynomial:

\[ p(-2) = (-2)^3 - 5(-2)^2 + 5(-2) + 10 \]

Calculating each term:

\[ = -8 - 5(4) - 10 + 10 \]
\[ = -8 - 20 - 10 + 10 \]
\[ = -8 - 20 \]
\[ = -28 \]

So, \( p(-2) = -28 \).

### Step 3: Add \( p(2) \) and \( p(-2) \)

Now we add the results from Step 1 and Step 2:

\[ p(2) + p(-2) = 8 + (-28) \]
\[ = 8 - 28 \]
\[ = -20 \]

### Final Answer

Thus, the final result is:

\[ p(2) + p(-2) = -20 \]