Multiply :
`x^(2) + x + 1` by `1-x`

Answer

To multiply the algebraic expression \( x^2 + x + 1 \) by \( 1 - x \), we will use the distributive property (also known as the FOIL method for binomials). Here’s a step-by-step solution:

### Step 1: Write down the expressions to be multiplied
We need to multiply:
\[ (x^2 + x + 1) \times (1 - x) \]

### Step 2: Distribute each term in the first expression by each term in the second expression
We will distribute \( x^2 \), \( x \), and \( 1 \) from the first expression across \( 1 \) and \( -x \) from the second expression.

1. **Multiply \( x^2 \) by \( 1 \)**:
\[ x^2 \times 1 = x^2 \]

2. **Multiply \( x^2 \) by \( -x \)**:
\[ x^2 \times -x = -x^3 \]

3. **Multiply \( x \) by \( 1 \)**:
\[ x \times 1 = x \]

4. **Multiply \( x \) by \( -x \)**:
\[ x \times -x = -x^2 \]

5. **Multiply \( 1 \) by \( 1 \)**:
\[ 1 \times 1 = 1 \]

6. **Multiply \( 1 \) by \( -x \)**:
\[ 1 \times -x = -x \]

### Step 3: Combine all the results
Now we combine all the results from the multiplications:
\[ x^2 - x^3 + x - x^2 + 1 - x \]

### Step 4: Simplify the expression
Now we will combine like terms:
- The \( x^2 \) and \( -x^2 \) cancel each other out:
\[ x^2 - x^2 = 0 \]
- The \( x \) and \( -x \) also cancel each other out:
\[ x - x = 0 \]

So we are left with:
\[ - x^3 + 1 \]

### Final Result
Rearranging gives us:
\[ 1 - x^3 \]

Thus, the final answer is:
\[ \boxed{1 - x^3} \]