a) (x+y)2 - (x-y)2
=(x2+2xy+y2) - (x2 - 2xy +y2)
=x2+2xy+y2 - x2 + 2xy -y2
=4xy
b) (a+b)3 + (a-b)3 -2a3
= (a3+3a2b+3ab2+b3 )+(a3-3a2b+3ab2-b3)-2a3
= a3+3a2b+3ab2+b3 +a3-3a2b+3ab2-b3 -2a3
=(a3 +a3 -2a3 ) + (3a2b -3a2b)+(3ab2+3ab2 ) +(b3 -b3)
=6ab2
c)98.28 -(184 -1)(184 +1)
=(9.2)8- [(184)2 -12 ]
=188 - 188 + 12 = 1
a, \((x+y)^2-(x-y)^2\)
\(= x^2+2xy+y^2-x^2-(x^2-2xy+y^2)\)
\(= x^2+2xy+y^2-x^2+2xy-y^2\)
\(= 4xy\)
b, \((a+b)^3+(a-b)^3 -2a^3\)
\(= a^3 + 3a^2b + 3ab^2 +b^3 - ( a^3 - 3a^2b + 3ab^2 - b^3 ) - 2b^3 \)
\(= a^3 +3a^2b +3ab^2 +b^3 -a^3 +3a^2b -3ab^2 +b^3 - 2b^3\)
\(=6a^2b\)
c, \(9^8 . 2^8 - ( 18^4 - 1 )( 18^4 + 1 )\)
\(= ( 9 . 2 )^8 - ( 18^8 - 1 )\)
\(= 18^8 - 18^8 + 1\)
\(= 1\)