The LCM of `(x+a)^(2) and (x^(2)-a^(2))` is ___________.

Answer

To find the LCM of the polynomials \( (x + a)^2 \) and \( (x^2 - a^2) \), we will follow these steps:

### Step 1: Factor the given polynomials
- The first polynomial is \( (x + a)^2 \), which can be expressed as:
\[ (x + a)(x + a) \]

- The second polynomial is \( (x^2 - a^2) \). This is a difference of squares and can be factored as:
\[ (x + a)(x - a) \]

### Step 2: Identify the factors
From the factorizations, we have:
- From \( (x + a)^2 \): the factor is \( (x + a) \) with a power of 2.
- From \( (x^2 - a^2) \): the factors are \( (x + a) \) and \( (x - a) \) with a power of 1 for \( (x + a) \) and 1 for \( (x - a) \).

### Step 3: Determine the LCM
To find the LCM, we take the highest power of each factor present in the factorizations:
- For the factor \( (x + a) \), the maximum power is 2 (from \( (x + a)^2 \)).
- For the factor \( (x - a) \), the maximum power is 1 (from \( (x^2 - a^2) \)).

Thus, the LCM is:
\[ \text{LCM} = (x + a)^2 (x - a) \]

### Final Answer
The LCM of \( (x + a)^2 \) and \( (x^2 - a^2) \) is:
\[ (x + a)^2 (x - a) \]

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