If `a = 23 and b= - 29` then the value of `25 a^(2)+40 ab + 16 b^(2)` is

Options

A. (a) 1
B. (b) `-1`
C. (c) 0
D. (d) 2

Answer

To solve the expression \( 25a^2 + 40ab + 16b^2 \) given \( a = 23 \) and \( b = -29 \), we will follow these steps:

### Step 1: Substitute the values of \( a \) and \( b \)
We start by substituting \( a = 23 \) and \( b = -29 \) into the expression:

\[ 25(23)^2 + 40(23)(-29) + 16(-29)^2 \]

### Step 2: Calculate \( 23^2 \) and \( -29^2 \)
Now, we calculate \( 23^2 \) and \( -29^2 \):

\[ 23^2 = 529 \]
\[ (-29)^2 = 841 \]

### Step 3: Substitute the squares back into the expression
Now we can substitute these values back into the expression:

\[ 25(529) + 40(23)(-29) + 16(841) \]

### Step 4: Calculate each term
Now we calculate each term separately:

1. \( 25(529) = 13225 \)
2. \( 40(23)(-29) = 40 \times 23 \times -29 = -26640 \)
3. \( 16(841) = 13456 \)

### Step 5: Combine all the terms
Now we combine all the calculated terms:

\[ 13225 - 26640 + 13456 \]

### Step 6: Perform the addition and subtraction
Calculating this step-by-step:

1. \( 13225 - 26640 = -13415 \)
2. \( -13415 + 13456 = 41 \)

### Final Result
Thus, the value of \( 25a^2 + 40ab + 16b^2 \) is:

\[ \boxed{41} \]