帮我做做下面几道题,a-a^3x^3-xy^34x^3y^3-9xy4x^2-8x-12y-9y^2已知a^2+b^2=5c^2+d^2=2求代数值（ac+bd）^2+(ad-bc)^2

Question

帮我做做下面几道题,
a-a^3
x^3-xy^3
4x^3y^3-9xy
4x^2-8x-12y-9y^2
已知a^2+b^2=5c^2+d^2=2求代数值（ac+bd）^2+(ad-bc)^2

Answer 1

a-a^3
=a(1-a^2)
=a(1+a)(1-a)
x^3y-xy^3
=x(x^2-y^2)
=x(x+y)(x-y)
4x^3y^3-9xy
=xy(4x^2y^2-9)
=xy(2xy+3)(2xy-3)
4x^2-8x-12y-9y^2
=4x^2-8x+4-(9y^2+12y+4)
=4(x-1)^2-(3y+2)^2
=(2x-2+3y+2)(2x-2-3y-2)
=(2x+3y)(2x-3y-4)