Question

现定义一种新的运算“*”,规定a*b+2a-b(a、b为整式）.当a=X²-y²,b=x²

Answer 1

现定义一种新的运算“*”,规定a*b=2a-b(a、b为整式）.

当a=X²-y²,b=x²+y²,c=2xy+y²时,求下列各式的值

（1）a*c

=2a-c

=2x^2-2y^2-(2xy+y^2)

=2x^2-2xy-3y^2

（2）a*(b*c)

=a*(2b-c)

=a*(2x^2+2y^2-2xy-y^2)

=a*(2x^2+y^2-2xy)

=2(x^2-y^2)-(2x^2+y^2-2xy)

=2x^2-2y^2-2x^2-y^2+2xy

=-3y^2+2xy