Find the product of 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 .

Given, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 Using the algebraic identity, ( a + b ) ( a – b ) = a 2 – b 2 We get, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 = 5 x 2 2 - 3 4 y 2 2 = 25 x 4 - 9 16 y 4 Thus, 5 x 2 + 3 4 y 2 5 x 2 - 3 4 y 2 = 25 x 4 - 9 16 y 4 .

Find the product of 4 x 5 - 5 y 3 4 x 5 + 5 y 3 .

Given, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 By using the formula, ( a + b ) ( a – b ) = a 2 – b 2 We get, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 = 4 x 5 2 - 5 y 3 2 = 16 25 x 2 - 25 9 y 2 . Thus, 4 x 5 - 5 y 3 4 x 5 + 5 y 3 = 16 25 x 2 - 25 9 y 2 .

Find the product of x + 1 x x - 1 x .

Given, x + 1 x x - 1 x By using the algebraic identity, ( a + b ) ( a – b ) = a 2 – b 2 , we have x + 1 x x - 1 x = x 2 - 1 x 2 = x 2 - 1 x 2 Thus, x + 1 x x - 1 x = x 2 - 1 x 2 .

Find the products of 1 x + 1 y 1 x - 1 y .

Given, 1 x + 1 y 1 x - 1 y We know that, ( a - b ) ( a + b ) = a 2 - b 2 Using this formula we get, 1 x + 1 y 1 x - 1 y = 1 x 2 - 1 y 2 = 1 x 2 - 1 y 2 Thus, 1 x + 1 y 1 x - 1 y = 1 x 2 - 1 y 2 .

Find the product of 2 a + 3 b 2 a - 3 b .

Given, 2 a + 3 b 2 a - 3 b Using the algebraic identity, ( a - b ) ( a + b ) = a 2 - b 2 2 a + 3 b 2 a - 3 b = 2 a 2 - 3 b 2 = 4 a 2 - 9 b 2 Thus, 2 a + 3 b 2 a - 3 b = 4 a 2 - 9 b 2 .