If p = 3, q = 2 and r = -1, find the values of
`2p^(2)+3a^(2)-r^(2)+2pr-5pqr`

Answer

To solve the expression \(2p^2 + 3q^2 - r^2 + 2pr - 5pqr\) given that \(p = 3\), \(q = 2\), and \(r = -1\), we will follow these steps:

### Step 1: Substitute the values of \(p\), \(q\), and \(r\) into the expression.

The expression is:
\[ 2p^2 + 3q^2 - r^2 + 2pr - 5pqr \]

Substituting \(p = 3\), \(q = 2\), and \(r = -1\):
\[ 2(3)^2 + 3(2)^2 - (-1)^2 + 2(3)(-1) - 5(3)(2)(-1) \]

### Step 2: Calculate each term.

1. Calculate \(2(3)^2\):
\[ 2 \times 9 = 18 \]

2. Calculate \(3(2)^2\):
\[ 3 \times 4 = 12 \]

3. Calculate \(-(-1)^2\):
\[ -1 = -1 \]

4. Calculate \(2(3)(-1)\):
\[ 2 \times 3 \times -1 = -6 \]

5. Calculate \(-5(3)(2)(-1)\):
\[ -5 \times 3 \times 2 \times -1 = 30 \]

### Step 3: Combine all the calculated terms.

Now we combine all the results:
\[ 18 + 12 - 1 - 6 + 30 \]

### Step 4: Simplify the expression.

1. Combine \(18 + 12\):
\[ 30 \]

2. Now, combine \(30 - 1\):
\[ 29 \]

3. Next, combine \(29 - 6\):
\[ 23 \]

4. Finally, combine \(23 + 30\):
\[ 53 \]

### Final Result:
The value of the expression is \(53\).

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