因式分解 (1) ax^4-81a (2) 4x^2(x-y)+2x(x-y) (3) a^2x^2+4a^2xy+4a^2y^2
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(1) ax^4-81a
=a(x^4-81)
=a(x²+9)(x²-9)
=a(x²+9)(x+3)(x-3)
(2) 4x^2(x-y)+2x(x-y)
=2x(x-y)(2x+1)
(3) a^2x^2+4a^2xy+4a^2y^2
=a²(x²+4xy+4y²)
=a²(x+2y)²
=a(x^4-81)
=a(x²+9)(x²-9)
=a(x²+9)(x+3)(x-3)
(2) 4x^2(x-y)+2x(x-y)
=2x(x-y)(2x+1)
(3) a^2x^2+4a^2xy+4a^2y^2
=a²(x²+4xy+4y²)
=a²(x+2y)²
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