Factorise:
`15ab ^(2) - 20 a ^(2)b`

Options

A. `5 ab (3b-4a )`
B. `6 ab (3b-4a )`
C. `5 ab (7b-4a )`
D. `5 ab (3b-5a )`

Answer

To factorise the expression \( 15ab^2 - 20a^2b \), 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 \( 15ab^2 \) and \( 20a^2b \).

- The coefficients are 15 and 20. The greatest common factor (GCF) of 15 and 20 is 5.
- The variables in the first term are \( ab^2 \) and in the second term are \( a^2b \). The common variable factors are \( ab \) (the lowest power of \( a \) is \( a^1 \) and for \( b \) is \( b^1 \)).

### Step 2: Factor out the GCF
Now we can factor out the GCF, which is \( 5ab \).

\[ 15ab^2 - 20a^2b = 5ab(3b - 4a) \]

### Step 3: Write the final factorised form
The factorised form of the expression is:

\[ 5ab(3b - 4a) \]

### Final Answer:
Thus, the factorised expression is \( 5ab(3b - 4a) \).

---