Factorise :
`8a b^(2) + 12 a^(2)b`

Answer

To factorise the expression \( 8ab^2 + 12a^2b \), we will follow these steps:

### Step 1: Identify the common factors
First, we need to identify the common factors in both terms of the expression. The two terms are \( 8ab^2 \) and \( 12a^2b \).

- The coefficients are 8 and 12. The greatest common divisor (GCD) of 8 and 12 is 4.
- The variable \( a \) appears in both terms, with the lowest power being \( a^1 \).
- The variable \( b \) also appears in both terms, with the lowest power being \( b^1 \).

Thus, the common factor is \( 4ab \).

### Step 2: Factor out the common factor
Now, we will factor out \( 4ab \) from the expression:

\[ 8ab^2 + 12a^2b = 4ab(2b) + 4ab(3a) \]

### Step 3: Write the expression in factored form
Now, we can combine the factored terms:

\[ 8ab^2 + 12a^2b = 4ab(2b + 3a) \]

### Final Answer
The factorised form of the expression \( 8ab^2 + 12a^2b \) is:

\[ 4ab(2b + 3a) \]

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