Question

Find the product of (x²y² - 2)(1 - 2x²y²) and verify the result for x= -1 and y= 2

Answer 1

(x²y² - 2)(1 - 2x²y²) = x²y² - 2x²y²x²y² - 2​​​​​​ + 4x²y²

= 5x²y² - 2x⁴y⁴ - 2

LHS = (x²y² - 2)(1 - 2x²y²)

= [(-1)²(2)² - 2 ][1 - 2(-1)²(2)² ]

= [ 1*4 - 2 ][ 1 - 2*1*4]

= 2 x (1-8)

= 2 * -7 = -14

RHS = 5x²y² - 2x⁴y⁴ - 2

= 5(-1)²(2)² - 2(-1)⁴(2)⁴ - 2

= 5*1*4 - 2*1*16 - 2 [(-1)⁴ = -1 x -1 x -1 x -1 = 1]

= 20 -32 -2

= -12 - 2

= -14

Hence LHS = RHS