已知x平方-y平方=20,求[（x-y)平方+4xy][(x+y)平方-4xy]的值

Question

已知x平方-y平方=20,求[（x-y)平方+4xy][(x+y)平方-4xy]的值

Answer 1

[(x-y)^2+4xy][(x+y)^2-4xy]
=(x-y)^2(x+y)^2-4xy(x-y)^2+4xy(x+6)^2-16x^2y^2
=(x^2-y^2)^2-4xy(x^2+2xy+y^2-x^2+2xy-y^2)-16x^2y^2
=(x^2-y^2)^2-4xy*4xy+(4xy)^2
=(x^2-y^2)^2
把x^2-y^2=20代人(x^2-y^2)^2=20^2=400
所以所求代数式的值是400