Simplify : `4(a^(3)+a^(2)+a)-(5a+3)` and find its value for
`a= 0`

Answer

To simplify the expression \( 4(a^3 + a^2 + a) - (5a + 3) \) and find its value when \( a = 0 \), we can follow these steps:

### Step 1: Distribute the 4
First, we need to distribute the 4 across the terms inside the parentheses:
\[ 4(a^3 + a^2 + a) = 4a^3 + 4a^2 + 4a \]

### Step 2: Rewrite the expression
Now, we can rewrite the entire expression by substituting the distributed terms:
\[ 4a^3 + 4a^2 + 4a - (5a + 3) \]

### Step 3: Distribute the negative sign
Next, we distribute the negative sign across the terms in the parentheses:
\[ 4a^3 + 4a^2 + 4a - 5a - 3 \]

### Step 4: Combine like terms
Now, we combine the like terms:
\[ 4a^3 + 4a^2 + (4a - 5a) - 3 = 4a^3 + 4a^2 - a - 3 \]

### Step 5: Substitute \( a = 0 \)
Now, we substitute \( a = 0 \) into the simplified expression:
\[ 4(0)^3 + 4(0)^2 - (0) - 3 \]

### Step 6: Calculate the value
Calculating this gives us:
\[ 0 + 0 - 0 - 3 = -3 \]

### Final Answer
Thus, the value of the expression when \( a = 0 \) is:
\[ \boxed{-3} \]