利用平方差公式计算大侠们1(4+3a)(-4+3a)2(2m-3n)(-2m-3n)3(-xy-3z)(3z-xy)4(x^4+y^4)(x^2+y^2)(x+y)(x-y)5(2/3x^2+1/2y^3)(1/2y^3-2/3x^2)6x^2(x+1)(x-1)+x^2

Question

利用平方差公式计算 大侠们
【1】(4+3a)(-4+3a) 【2】(2m-3n)(-2m-3n) 【3】(-xy-3z)(3z-xy) 【4】(x^4+y^4)(x^2+y^2)(x+y)(x-y) 【5】(2/3 x^2+1/2 y^3)(1/2 y^3-2/3 x^2) 【6】x^2(x+1)(x-1)+x^2

Answer 1

1】(4+3a)(-4+3a)
=9a^2-16
【2】(2m-3n)(-2m-3n)
=(3n-2m)(3n+2m)
=9n^2-4m^2
【3】(-xy-3z)(3z-xy)
=(-xy)^2-9z^2
=x^2y^2-9z^2
【4】(x^4+y^4)(x^2+y^2)(x+y)(x-y)
=(x^4+y^4)(x^2+y^2)(x^2-y^2)
=(x^4+y^4)(x^4-y^4)
=x^8-y^8
【5】(2/3 x^2+1/2 y^3)(1/2 y^3-2/3 x^2)
=(1/2 y^3)^2-(2/3 x^2)^2
=1/4y^6-4/9x^4
【6】x^2(x+1)(x-1)+x^2
=x^2(x^2-1)+x^2
=X^4