Question

find the following product and verify the result for x=-1,y=2 (x^2y^2-2)(1-2x^2y^2)​

Answer 1

Answer:

(x²y²-2)(1-2x²y²) = (-1²×2²-2)×(1-2×-1²×2²)

= (4-2)(1+2×4)

= 2 × 9

= 18

Answer 2

Answer:

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Find the product of x2 y2 21 2 x2 y2 and verify the result for x= 1 and y=2

Question

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

Solution

(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