Identity \(- 4\): (a + b)(a − b)= a2b2
Let us first, simplify the identity (a + b)(a − b)= a2b2.
Multiply the expression, as shown below.
pic 1.png
Now, we construct a figure to understand the concept.
pic 3.png
Then we construct a rectangle using the above information.
In the given figure, \(AB = AD = a\).

So, the area of square \(ABCD = a^2\).
pic 2.png
Also, \(SB = DP = b\). Then the area of the rectangle \(SBCT = ab\).
Similarly, the area of the rectangle \(DPRC = ab\). And the area of the square \(TQRC = b^2\).
Area of the rectangle \(DPQT = ab − b^2\).
Hence, \(\text{the area of the rectangle APQS = The area of square ABCD}\) \(\text{– area of rectangle STCB}\) \(\text{+ area of rectangle DPQT}\).
Therefore, (a + b)(a − b)= a2b2.
Simplify (3x + 9)(3x  9) using the identity.
First, develop the given (3x + 9)(3x  9) expression using the identity (a + b)(a − b)= a2b2.
Here, \(a = 3x\); \(b = 9y\).
(3x + 9)(3x9)=(3x)2(9)2=32×x2(9)2=9x281
Therefore, (3x + 9)(3x  9) \(=\) 9\(x^2 -\)81.