分解因式(1)a3次方-16a (2)16(a+b)方-9(a-b)方 (3)x的4次方-81 (4)(2x+y)方-(x+2y)方

解：
(1)a3次方-16a
=a(a²-16)
=a(a+4)(a-4)
(2)16(a+b)方-9(a-b)方
=(4a+4b)²-(3a-3b)²
=(4a+4b-3a+3b)(4a+4b+3a-3b)
=(a+7b)(7a+b)
(3)x的4次方-81
=(x²-9)(x²+9)
=(x-3)(x+3)(x²+9)
(4)(2x+y)方-(x+2y)方
=(2x+y+x+2y)(2x+y-x-2y)
=3(x+y)(x-y)
(5)9(x-3)方-4(2-3x)方
=(3x-9)²-(4-6x)²
=(3x-9+4-6x)(3x-9-4+6x)
=(-3x-5)(9x-13)
=-(3x+5)(9x-13)
(6)-4(x-y)方+16z方
=4[(2z)²-(x-y)²]
=4(2z-x+y)(2z+x-y)

如仍有疑惑，欢迎追问。 祝：学习进步！

(1)a3次方-16a
=a(a^2-16)
=a(a+4)(a-4)
(2)16(a+b)方-9(a-b)方
=[4(a+b)+3(a-b)][(4(a+b)-3(a-b)]
=(7a+b)(a+7b)
(3)x的4次方-81
=(X^2-9)(X^2+9)=(X+3)(X-3)(X^2+9)
(4)(2x+y)方-(x+2y)方
=[(2X+Y)+(X+2Y)][(2X+Y)-(X+2Y)]
=(3X+3Y)(X-Y)
=3(X+Y)(X-Y)
.(5)9(x-3)方-4(2-3x)方
=[3(X-3)+2(2-3X)][3(X-3)-2(2-3X)]
=(-3X-5)(9X-13)=-(3X-5)(9X-13)
(6)-4(x-y)方+16z方
=-4[(X-Y)+2Z][(X-Y)-2Z]
=-4(X-Y+2Z)(X-Y-2Z).

1\a3次方-16a =a(a^2-16)=a(a+4)(a-4)

2\16(a+b)方-9(a-b)方=16a^2+32ab+16b^2-9a^2+18ab-9b^2
=7a^2+50ab+7b^2=(7a+b)(a+7b)

(3)x的4次方-81 =(x^2+9)(x^2-9)=(x^2+9)(x+3)(x-3)

(4)(2x+y)方-(x+2y)方=4x^2+4xy+y^2-x^2-4xy-4y^2=3x^2-3y^2=3(x^2-y^2)=3(x+y)(x-y)
希望可以帮到你，满意请采纳

1、a(a+4)(a-4)
2 (4a+4b-3a+3b)(4a+4b+3a-3b)=(a+7b)(7a+b)
3 (3x-y)(x+3y)
4 (-3x-5)(9x-13)
5 (4z+2x-2y)(4z-2x+2y)

这个考察的主要是a^2-b^2=(a+b)(a-b) 的知识 只要准确运用这个公式就可以了