103^2-97^2
=(103+97)(103-97)
=200.6
=1200
556^2-553.559
=556^2-(556^2-3^2)
=3^2
 

1A.
a) 103^2- 97^2 = (103 - 97)(103 + 97) = 6.200 = 1200
b) 556^2 - 553.559 = 309136 - 309127 = 9
c) 456^2 + 456.88 + 44^2 = (456 + 44)^2 = 500^2 = 250000

1B. 
a) 202.198 = (200 + 2)(200 - 2) = 200^2 - 2^2 = 40000 - 4 = 39996
b) 662.668 - 665^2 = (665 - 3)(665 + 3) - 665^2
= 665^2 - 3^2 - 665^2 = -9
c) 678^2 - 356.678 + 178^2 = (678 - 178)^2 = 500^2 = 250000

2A.
a) A = 4.x^2 - 4x + 1 = (2x - 1)^2
= (2.5,5 - 1)^2 = (11 - 1)^2 = 10^2 = 100
b) B = x^3 - 6.x^2 + 12x - 7 = (x - 2)^3 + 1
= (12 - 2)^3 + 1 = 10^3 + 1 = 1000 + 1 = 1001
c) 8.x^3 - 12.x^2.y + 6x.y^2 - y^3
= (2x - y)^3 = (2.19 - 39)^3 = (-1)^3 = -1

2B.
a) A = y^2 - 12y + 36 = (y - 6)^2
= (16 - 6)^2 = 10^2 = 100
b) 27.x^3 + 27.x^2 + 9x + 11
= (3x + 1)^3 + 10
= (3.19/3 + 1)^3 + 10
= 20^3 + 10 = 8000 + 10 = 8010
c) 8.y^3 - 36.y^2.z + 54y.z^2 - 27.z^3
= (2y - 3z)^3 = (2.50 - 3.33)^3 = 1^3 = 1