1. Find the following products: 1.1 (2a - 3)(2a + 3) = 1.2 (ba - 2)(ba + 2) = 1.3 (8a - 1)(8a + 1) = 1.4 (5 - 3p^2)(5 + 3p^2) =

To find the products of these binomials, we can use the difference of squares formula. This formula states that for any two terms a and b , ( a − b ) ( a + b ) = a 2 − b 2 . Let's apply this step-by-step to each part:
1.1 (2a - 3)(2a + 3)
Using the formula: ( 2 a ) 2 − 3 2 = 4 a 2 − 9
Therefore, the product is 4 a 2 − 9 .
1.2 (ba - 2)(ba + 2)
Applying the formula: ( ba ) 2 − 2 2 = b 2 a 2 − 4
Hence, the product is b 2 a 2 − 4 .
1.3 (8a - 1)(8a + 1)
Using the formula: ( 8 a ) 2 − 1 2 = 64 a 2 − 1
The product is 64 a 2 − 1 .
1.4 (5 - 3p^2)(5 + 3p^2)
Applying the formula: 5 2 − ( 3 p 2 ) 2 = 25 − 9 p 4
Thus, the product is 25 − 9 p 4 .
Each of these calculations uses the properties of the difference of squares to find a simpler expression for the product of two binomials. This method is useful because it streamlines the computation and highlights the symmetry in the binomials' structure.

Answered by MasonWilliamTurner | 2025-07-21