(1)16（x-y）^2-9(x+y)^2
=[4(x-y)]^2-[3(x+y)]^2
=[4(x-y)-3(x+y)]^2
=(x-7y)^2
(2)4(2p+3q)^2-(3p-q)^2
=[2(2p+3q)]^2-(3p-q)^2
=[2(2p+3q)-(3p-q)]^2
=(p+7q)^2
(3)169(a-b)^2-196(a+b)^2
=[13(a-b)]^2-[14(a+b)]^2
=[13(a-b)-14(a+b)]^2
=(a+27b)^2
【（a+1/2）^2+(a-1/2)^2】*（2a^2-1/2b^2)
=[（a+1/2）+(a-1/2)]^2*(2a+1)(2a-1)/2b^2
=(2a)^2*(2a+1)(2a-1)/2b^2
=a^2(2a+1)(2a-1)/b^2
其中a=-3,b=4
原式=(-3)^2[2*(-3)+1][2*(-3)-1]/4^2
=9*(-5)*(-7)/16
=305/16