Factorise:
` 8 (4x + 5y)^(2) - 12 (4x + 5y)`

Options

A. ` 4 (4x - 5 y) (8x + 10y-3)`
B. ` 4 (4x + 5 y) (8x + 10y +3)`
C. ` 4 (4x + 5 y) (8x + 10y-3)`
D. none of these

Answer

To factorise the expression \( 8(4x + 5y)^2 - 12(4x + 5y) \), we can follow these steps:

### Step 1: Identify the common factor
We can see that both terms in the expression share a common factor of \( (4x + 5y) \).

### Step 2: Factor out the common term
We can factor out \( (4x + 5y) \) from the expression:
\[ 8(4x + 5y)^2 - 12(4x + 5y) = (4x + 5y)(8(4x + 5y) - 12) \]

### Step 3: Simplify the expression inside the parentheses
Now, simplify the expression inside the parentheses:
\[ 8(4x + 5y) - 12 \]
This can be simplified further:
\[ = 8(4x + 5y) - 12 = 8(4x + 5y) - 12 \cdot 1 \]

### Step 4: Factor out the numeric coefficient
Next, we can factor out the common numeric coefficient from the second term:
\[ = 4(2(4x + 5y) - 3) \]
Thus, we have:
\[ = (4x + 5y)(4(2(4x + 5y) - 3)) \]

### Step 5: Write the final factorised form
Now we can write the final factorised form:
\[ = 4(4x + 5y)(2(4x + 5y) - 3) \]

### Final Answer
The factorised form of the expression \( 8(4x + 5y)^2 - 12(4x + 5y) \) is:
\[ 4(4x + 5y)(2(4x + 5y) - 3) \]

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