分解公因式-a^4+16-x^2+4xy-4y^2ax^2+2a^2x+a^3-3x^2+6xy-3y^24xy^2-4x^2y-y^3(p-4)(p+1)+3px^2+7x-18(a-b)(x-y)-(b-a)(x+y)6xy^2-9x^2y-y^33x^2+27x-54

Question

分解公因式 -a^4+16
-x^2+4xy-4y^2
ax^2+2a^2x+a^3
-3x^2+6xy-3y^2
4xy^2-4x^2y-y^3
(p-4)(p+1)+3p
x^2+7x-18
(a-b)(x-y)-(b-a)(x+y)
6xy^2-9x^2y-y^3
3x^2+27x-54

Answer 1

-x^2+4xy-4y^2=-(x^2-4xy+4y^2)=-(x-2y)^2
ax^2+2a^2x+a^3=a(x^2+2ax+a^2)=a(x+a)^2
-3x^2+6xy-3y^2=-3(x^2-2xy+y^2)=-3(x-y)^2
4xy^2-4x^2y-y^3=-y(4x^2-4xy+y^2)=-y(2x-y)^2
(p-4)(p+1)+3p=p^2-3p-4+3p=p^2-4=(p+2)(p-2)
x^2+7x-18=(x+9)(x-2)
(a-b)(x-y)-(b-a)(x+y)=(a-b)[(x-y)+(x+y)]=2x(a-b)
6xy^2-9x^2y-y^3=-y(9x^2-6xy+y^2)=-y(3x-y)^2
3x^2+27x-54=3(x^2+9x-18)