Evaluate :
`xy^(2) (x-5y) + 1` for x = 2 and y= 1.

Answer

To evaluate the expression \( xy^2 (x - 5y) + 1 \) for \( x = 2 \) and \( y = 1 \), follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \)
We start by substituting \( x = 2 \) and \( y = 1 \) into the expression.

\[ xy^2 (x - 5y) + 1 = (2)(1^2)(2 - 5 \cdot 1) + 1 \]

### Step 2: Calculate \( y^2 \)
Next, we calculate \( y^2 \).

\[ 1^2 = 1 \]

### Step 3: Substitute \( y^2 \) back into the expression
Now, substitute \( y^2 \) back into the expression.

\[ = (2)(1)(2 - 5 \cdot 1) + 1 \]

### Step 4: Calculate \( 5y \)
Now, calculate \( 5y \).

\[ 5 \cdot 1 = 5 \]

### Step 5: Substitute \( 5y \) back into the expression
Substituting \( 5y \) back into the expression gives us:

\[ = (2)(1)(2 - 5) + 1 \]

### Step 6: Simplify the expression inside the parentheses
Now, simplify \( 2 - 5 \).

\[ 2 - 5 = -3 \]

### Step 7: Substitute back into the expression
Substituting this back gives:

\[ = (2)(1)(-3) + 1 \]

### Step 8: Calculate the product
Now, calculate the product:

\[ (2)(1)(-3) = -6 \]

### Step 9: Add 1 to the result
Finally, add 1 to the result:

\[ -6 + 1 = -5 \]

### Final Answer
Thus, the value of the expression \( xy^2 (x - 5y) + 1 \) for \( x = 2 \) and \( y = 1 \) is:

\[ \boxed{-5} \]