Factorise:
`1+ a + ac + a^(2)c`

Options

A. `(1 - a)(1 + ac)`
B. `(1 + a)(1 + ac)`
C. `a(1 + ac)`
D. None of these

Answer

To factorise the expression \(1 + a + ac + a^2c\), we can follow these steps:

### Step 1: Group the terms
We can group the terms in pairs to make it easier to factor. We can group \(1 + a\) and \(ac + a^2c\).

\[ (1 + a) + (ac + a^2c) \]

### Step 2: Factor out the common terms
Now, we can factor out the common terms from each group. The first group \(1 + a\) remains as it is, and from the second group \(ac + a^2c\), we can factor out \(ac\).

\[ (1 + a) + ac(1 + a) \]

### Step 3: Factor out the common binomial
Now we see that both terms have a common factor of \(1 + a\). We can factor \(1 + a\) out.

\[ (1 + a)(1 + ac) \]

### Final Result
Thus, the factorised form of the expression \(1 + a + ac + a^2c\) is:

\[ (1 + a)(1 + ac) \]

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