Factorise:
`10x ^(3)-15 x ^(2)`

Answer

To factorise the expression \(10x^3 - 15x^2\), we will follow these steps:

### Step 1: Identify the common factors
First, we need to identify the common factors in the terms \(10x^3\) and \(15x^2\).

- The coefficients are 10 and 15. The greatest common factor (GCF) of 10 and 15 is 5.
- For the variable part, \(x^3\) and \(x^2\), the common factor is \(x^2\) (the lowest power of x).

### Step 2: Factor out the common factors
Now, we will factor out the GCF, which is \(5x^2\).

\[ 10x^3 - 15x^2 = 5x^2(2x) - 5x^2(3) \]

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

\[ 10x^3 - 15x^2 = 5x^2(2x - 3) \]

### Final Answer
Thus, the factorised form of \(10x^3 - 15x^2\) is:

\[ 5x^2(2x - 3) \]

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