Factorise by taking out the common factors :
`2(2x - 5y)(3x + 4y) - 6(2x - 5y)(x-y)`

Answer

To factorise the expression \( 2(2x - 5y)(3x + 4y) - 6(2x - 5y)(x - y) \), we can follow these steps:

### Step 1: Identify the Common Factor
We can see that \( (2x - 5y) \) is a common factor in both terms of the expression.

### Step 2: Factor Out the Common Factor
We can factor out \( (2x - 5y) \) from the expression:
\[ 2(2x - 5y)(3x + 4y) - 6(2x - 5y)(x - y) = (2x - 5y) \left[ 2(3x + 4y) - 6(x - y) \right] \]

### Step 3: Simplify the Expression Inside the Brackets
Now, we simplify the expression inside the brackets:
\[ 2(3x + 4y) - 6(x - y) = 6x + 8y - 6x + 6y \]
Combine like terms:
\[ 6x - 6x + 8y + 6y = 14y \]

### Step 4: Write the Final Factored Form
Now, substituting back into the factored form, we have:
\[ (2x - 5y)(14y) \]

### Final Answer
Thus, the expression \( 2(2x - 5y)(3x + 4y) - 6(2x - 5y)(x - y) \) can be factored as:
\[ 14y(2x - 5y) \]

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