Answer in true or false:
`(a+b)xx (a+c) = a+(b+c)`

Answer

To determine whether the expression \((a+b) \times (a+c) = a + (b+c)\) is true or false, we will analyze both sides of the equation step by step.

### Step 1: Understand the Left-Hand Side (LHS)
The left-hand side of the equation is \((a+b) \times (a+c)\).

### Step 2: Expand the LHS
Using the distributive property (also known as the FOIL method for binomials), we can expand the left-hand side:

\[ (a+b) \times (a+c) = a \times (a+c) + b \times (a+c) \]

### Step 3: Distribute Each Term
Now we will distribute \(a\) and \(b\) across \((a+c)\):

\[ = a^2 + ac + ab + bc \]

So, the expanded form of the left-hand side is:

\[ LHS = a^2 + ab + ac + bc \]

### Step 4: Understand the Right-Hand Side (RHS)
The right-hand side of the equation is \(a + (b+c)\).

### Step 5: Simplify the RHS
The right-hand side can be simplified as follows:

\[ RHS = a + b + c \]

### Step 6: Compare LHS and RHS
Now we compare the two sides:

- LHS: \(a^2 + ab + ac + bc\)
- RHS: \(a + b + c\)

### Step 7: Determine if They are Equal
Clearly, \(a^2 + ab + ac + bc\) is not equal to \(a + b + c\). Therefore, the two sides are not equal.

### Conclusion
Since the left-hand side does not equal the right-hand side, we conclude that the statement \((a+b) \times (a+c) = a + (b+c)\) is **False**.

### Final Answer
**False**

---