Find the value of the expression `25 x^(2) + 9y^(2) + 30 xy`. When x = 8 and y = 10.

Answer

To find the value of the expression \( 25x^2 + 9y^2 + 30xy \) when \( x = 8 \) and \( y = 10 \), we can follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \) into the expression.
We have:
\[ x = 8 \quad \text{and} \quad y = 10 \]
Substituting these values into the expression gives:
\[ 25(8^2) + 9(10^2) + 30(8)(10) \]

### Step 2: Calculate \( x^2 \) and \( y^2 \).
Calculating \( 8^2 \) and \( 10^2 \):
\[ 8^2 = 64 \quad \text{and} \quad 10^2 = 100 \]

### Step 3: Substitute the squared values back into the expression.
Now substituting these squared values back into the expression:
\[ 25(64) + 9(100) + 30(8)(10) \]

### Step 4: Calculate each term.
Calculating each term:
1. \( 25(64) = 1600 \)
2. \( 9(100) = 900 \)
3. \( 30(8)(10) = 2400 \)

### Step 5: Add all the terms together.
Now, we add all the calculated values:
\[ 1600 + 900 + 2400 \]

### Step 6: Perform the addition.
Calculating the sum:
\[ 1600 + 900 = 2500 \]
\[ 2500 + 2400 = 4900 \]

### Final Answer:
Thus, the value of the expression \( 25x^2 + 9y^2 + 30xy \) when \( x = 8 \) and \( y = 10 \) is:
\[ \boxed{4900} \]

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