Question

几题数学初二题.分解因式.要过程

(1)3ax的立方-108ax
(2)81a的4次方-1
(3)(5a-b)的平方+20ab
(4)16x的立方-4x
(5)2x的平方y-8xy+8y
(6)3a(x-y)-5b(y-x)

Answer 1

解:(1)3ax的立方-108ax=3ax(x^2-36)=3ax(x-6)(x+6)
(2)81a的4次方-1=(9a^2-1)(9a^2+1)=(3a-1)(3a+1)(9a^2+1)
(3)(5a-b)的平方+20ab=25a^2-10ab+b^2+20ab=25a^2+10ab+b^2=(5a+b)^2
(4)16x的立方-4x=4x(4x^2-1)=4x(2x-1)(2x+1)
(5)2x的平方y-8xy+8y=2y(x^2-4x+4)=2y(x-2)^2
(6)3a(x-y)-5b(y-x)=3a(x-y)+5b(x-y)=(3a+5b)(x-y)

Answer 2

[1] 3ax^3-108ax=3ax(x^2-36)=3ax(x-6)(x+6)
[2]81a^4-1=(9a^2+1)(9a^2-1)=(9a^2+1)(3a+1)(3a-1)
[3](5a-b)^2+20ab=25a^2-10ab+b^2+20b=25a^2+10ab+b^2=(5a+b)^2
[4]16x^3-4x=4x(x^2-1)=4x(x+1)(x-1)
[5]2(x^2)y-8xy+8y=2y(x^2-4x+4)=2y(x-2)^2
[6]3a(x-y)-5b(y-x)=3ax-3ay-5by+5bx=(3a+5b)x-(3a+5b)y
注：^2就是平方 ^3就是立方，依次类推

Answer 3

1、原式=3ax(x^2-36)=3ax(x-6)(x+6).
2、原式=(9a^2+1)(9a^2-1)=(9a^+1)(3a+1)(3a-1).
3、原式=25a^2-10ab+b^2+20ab=(5a+b)^2.
4、原式=2y(x^2-4x+4)=2y(x-2)^2.
5、原式=(x-y)(3a+5b)..

Answer 4

解（1）3ax³-108ax
=3ax(x²-36)
=3ax(x+6)(x-6)
(2):81a^4-1
=(9a²+1)(9a²-1)
=(9a²+1)(3a+1)(3a-1)
(3):(5a-b)²+20ab
=25a²-10ab+b²+20ab
=25a²+10ab+b²
=(5a)²+2×5a×b+b²
=(5a+b)²
(4):16x³-4x
=4x(x²-1)
4x(x+1)(x-1)
(5):2x²y-8xy+8y
=2y(x²-4x+4)
=2y(x-2)²
(6):3a(x-y)-5b(y-x)
=3a(x-y)+5b(x-y)
=(x-y)(3a+5b)

Answer 5

(1):3ax(x+6)(x-6)
(2):(3a+1)(3a-1)(9a^2+1)
(3):(5a+b)(5a+b)
(4):4x(2x+1)(2x-1)
(5):2y(x-2)(x-2)
(6):(3a+5b)(x-y)