Factories : `64a^(2)+96ab+36b^(2)`

Answer

To factor the expression \(64a^2 + 96ab + 36b^2\), we can follow these steps:

### Step 1: Identify the coefficients and terms
The given expression is \(64a^2 + 96ab + 36b^2\). Here, we have:
- The coefficient of \(a^2\) is \(64\),
- The coefficient of \(ab\) is \(96\),
- The coefficient of \(b^2\) is \(36\).

### Step 2: Recognize perfect squares
We can recognize that:
- \(64a^2\) can be expressed as \((8a)^2\),
- \(36b^2\) can be expressed as \((6b)^2\).

### Step 3: Check the middle term
Now, we need to check if the middle term \(96ab\) fits the identity for a perfect square trinomial, which is of the form \(A^2 + 2AB + B^2\).

Here, we can set:
- \(A = 8a\),
- \(B = 6b\).

Now, we calculate \(2AB\):
\[ 2AB = 2 \cdot (8a) \cdot (6b) = 96ab. \]
This matches our middle term.

### Step 4: Write the expression as a square
Since the expression fits the form \(A^2 + 2AB + B^2\), we can write it as:
\[ (8a + 6b)^2. \]

### Final Answer
Thus, the factorization of \(64a^2 + 96ab + 36b^2\) is:
\[ (8a + 6b)^2. \]

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