Question

因式分解 急求！！~

81a^4-72a^2b^2+16b^4;(a^2+b^2)^2-4a^2b^2;8xy-x^2-16y^2;81-78(a+4)+(a+4)^2;-16x^2y^2+12xy^5z-8xz^3;a^n+2+a^n+1-6a^n

Answer 1

81a^4-72a^2b^2+16b^4
=(9a^2-4b^2)^2
=[(3a-2b)(3a+2b)]^2
=(3a-2b)^2(3a+2b)^2

(a^2+b^2)^2-4a^2b^2
=(a^2+b^2-2ab)(a^2+b^2+2ab)
=(a-b)^2(a+b)^2

8xy-x^2-16y^2
=-(x^2-8xy+16y^2)
=-(x-4y)^2

81-18(a+4)+(a+4)^2
=(a+4)^2-18(a+4)+81
=(a+4-9)^2
=(a-5)^2

-16x^2y^2+12xy^5z-8xz^3
=-4x(4xy^2-3y^5z+2z^3)

a^(n+2)+a^(n+1)-6a^n
=a^n*a^2+a^n*a-6a^n
=a^n(a^2+a-6)
=a^n(a+3)(a-2)

Answer 2

81a^4-72a^2b^2+16b^4
=(9a²-4b²)²
=(3a+2b)²(3a-2b)²

(a^2+b^2)^2-4a^2b^2
=(a²+b²+2ab)(a²+b²-2ab)
=(a+b)²(a-b)²

8xy-x^2-16y^2
=-(x²-8xy+16y²)
=-(x-4y)²

81-18(a+4)+(a+4)^2
=[9-(a+4)]²
=(5-a)²

-16x^2y^2+12xy^5z-8xz^3
=-4x(4xy²-3y^5z+2z^3)

a^n+2+a^n+1-6a^n
=a^n(a²+a-6)
=a^n(a+3)(a-2)