Expand ` (2a -4b +7) (2a+ 4b+7) `

Answer

To expand the expression \( (2a - 4b + 7)(2a + 4b + 7) \), we can follow these steps:

### Step 1: Rearrange the Expression
We can rearrange the terms in each bracket:
\[ (2a + 7 - 4b)(2a + 7 + 4b) \]

### Step 2: Recognize the Form
This expression can be recognized as a difference of squares, where:
- Let \( x = 2a + 7 \)
- Let \( y = 4b \)

Thus, we can rewrite the expression as:
\[ (x - y)(x + y) = x^2 - y^2 \]

### Step 3: Substitute Back
Now substitute back the values of \( x \) and \( y \):
\[ (2a + 7)^2 - (4b)^2 \]

### Step 4: Expand Each Square
Now we will expand each square:
1. For \( (2a + 7)^2 \):
\[ (2a + 7)^2 = (2a)^2 + 2 \cdot (2a) \cdot 7 + 7^2 = 4a^2 + 28a + 49 \]

2. For \( (4b)^2 \):
\[ (4b)^2 = 16b^2 \]

### Step 5: Combine the Results
Now substitute back into the expression:
\[ (2a + 7)^2 - (4b)^2 = (4a^2 + 28a + 49) - 16b^2 \]

### Step 6: Write the Final Answer
Thus, the final expanded form is:
\[ 4a^2 + 28a + 49 - 16b^2 \]

### Final Answer:
\[ 4a^2 + 28a + 49 - 16b^2 \]

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