Find the expansion of the using suitable identity.
`(3x +7y) (3x - 7y)`

Answer

To find the expansion of the expression \((3x + 7y)(3x - 7y)\) using a suitable identity, we can follow these steps:

### Step 1: Identify the Identity
We will use the identity for the difference of squares, which states:
\[ (a + b)(a - b) = a^2 - b^2 \]
In our case, we can identify:
- \(a = 3x\)
- \(b = 7y\)

### Step 2: Substitute into the Identity
Using the values of \(a\) and \(b\) in the identity, we can rewrite our expression:
\[ (3x + 7y)(3x - 7y) = (3x)^2 - (7y)^2 \]

### Step 3: Calculate \(a^2\) and \(b^2\)
Now, we calculate \(a^2\) and \(b^2\):
- \(a^2 = (3x)^2 = 9x^2\)
- \(b^2 = (7y)^2 = 49y^2\)

### Step 4: Write the Final Expression
Substituting \(a^2\) and \(b^2\) back into the equation gives us:
\[ (3x + 7y)(3x - 7y) = 9x^2 - 49y^2 \]

### Final Answer
Thus, the expansion of \((3x + 7y)(3x - 7y)\) is:
\[ 9x^2 - 49y^2 \]

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