`9x^2+12xy`

Answer

To factor the expression \(9x^2 + 12xy\), we can follow these steps:

### Step 1: Identify the common factors
Look at the coefficients and the variables in both terms:
- The coefficients are 9 and 12.
- The variable part includes \(x^2\) and \(xy\).

### Step 2: Find the greatest common factor (GCF)
The GCF of the coefficients 9 and 12 is 3.
For the variable part, the common factor is \(x\) (since both terms have at least one \(x\)).

### Step 3: Factor out the GCF
Now, we can factor out \(3x\) from both terms:
\[ 9x^2 + 12xy = 3x(3x) + 3x(4y) \]

### Step 4: Write the factored form
After factoring out \(3x\), we can rewrite the expression as:
\[ 9x^2 + 12xy = 3x(3x + 4y) \]

### Final Answer
Thus, the factored form of \(9x^2 + 12xy\) is:
\[ 3x(3x + 4y) \]

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