Simplify : `4(a^(3)+a^(2)+a)-(5a+3)` and find its value for
`a= 1`

Answer

To simplify the expression \( 4(a^3 + a^2 + a) - (5a + 3) \) and find its value for \( a = 1 \), we will follow these steps:

### Step 1: Distribute the 4
We start by distributing the 4 across the terms inside the parentheses:

\[ 4(a^3 + a^2 + a) = 4a^3 + 4a^2 + 4a \]

So, the expression becomes:

\[ 4a^3 + 4a^2 + 4a - (5a + 3) \]

### Step 2: Distribute the negative sign
Next, we distribute the negative sign across the terms in the parentheses:

\[ -(5a + 3) = -5a - 3 \]

Now, we can rewrite the expression:

\[ 4a^3 + 4a^2 + 4a - 5a - 3 \]

### Step 3: Combine like terms
Now, we combine the like terms. The like terms here are \( 4a \) and \( -5a \):

\[ 4a - 5a = -a \]

So, the expression simplifies to:

\[ 4a^3 + 4a^2 - a - 3 \]

### Step 4: Substitute \( a = 1 \)
Now, we will substitute \( a = 1 \) into the simplified expression:

\[ 4(1^3) + 4(1^2) - (1) - 3 \]

Calculating each term:

\[ 4(1) + 4(1) - 1 - 3 = 4 + 4 - 1 - 3 \]

### Step 5: Perform the arithmetic
Now we perform the addition and subtraction:

\[ 4 + 4 = 8 \]
\[ 8 - 1 = 7 \]
\[ 7 - 3 = 4 \]

Thus, the value of the expression when \( a = 1 \) is:

\[ \boxed{4} \]

---