问题1.分解64a 3 + 125b 3 + 240a 2 b + 300ab 2
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
(4a)3+(5b)3+3(4a)2(5b)+3(4a)(5b)2
(4a+5b)3
(4a+5b)(4a+5b)(4a+5b)
Hence, 64a3+125b3+240a2b+300ab2 = (4a+5b)(4a+5b)(4a+5b)
问题2.分解125x 3 -27y 3 -225x 2 y + 135xy 2
解决方案：
As we know that, a3 – b3-3a2b+3ab2 = (a-b)3
So, the above expression can be written as:
(5x)3-(3y)3-3(5x)2(3y)+3(5x)(3y)2
(5x-3y)3
(5x-3y)(5x-3y)(5x-3y)
Hence, 125x3-27y3-225x2y+135xy2 = (5x-3y)(5x-3y)(5x-3y)
问题3.分解8 / 27x 3 + 1 + 4 / 3x 2 + 2x
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
(2/3x)3+13+3(2/3x)2(1)+ 3(2/3x)(1)
(2/3x+1)3
(2/3x+1) (2/3x+1) (2/3x+1)
Hence, 8/27x3+1+4/3x2+2x = (2/3x+1) (2/3x+1) (2/3x+1)
问题4.分解8x 3 + 27y 3 + 36x 2 y + 54xy 2
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
(2x)3+(3y)3+3(2x)2(3y)+3(2x)(3y)2
(2x+3y)3
(2x+3y)(2x+3y)(2x+3y)
Hence, 8x3+27y3+36x2y+54xy2 = (2x+3y)(2x+3y)(2x+3y)
问题5比化3 -3a 2 B + 3AB 2 -b 3 8
解决方案：
As we know that, a3 – b3-3a2b+3ab2 = (a-b)3
So, the above expression can be written as:
(a-b)3 + (2)3
(a-b+2)[(a-b)2-(a-b)(2)+22]
Use a3+b3=(a+b)(a2-ab+b2)
(a-b+2)(a2+b2-2ab-2a+2b+4)
Hence, a3-3a2b+3ab2-b3+8 = (a-b+2)(a2+b2-2ab-2a+2b+4)
问题6.分解x 3 + 8y 3 + 6x 2 y + 12xy 2
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
x3+(2y)3+3(x)2(2y)+3(x)(2y)2
(x+2y)3
(x+2y)(x+2y)(x+2y)
Hence, x3+8y3+6x2y+12xy2 = (x+2y)(x+2y)(x+2y)
问题7：分解8x 3 + y 3 + 12x 2 y + 6xy 2
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
(2x)3 +y3+3(2x)2y+3(2x)(y)2
(2x+y)3
(2x+y)(2x+y)(2x+y)
Hence, 8x3+y3+12x2y+6xy2 = (2x+y)(2x+y)(2x+y)
问题8.分解8a 3 + 27b 3 + 36a 2 b + 54ab 2
解决方案：
As we know that, a3+b3+3a2b+3ab2 = (a+b)3
So, the above expression can be written as:
(2a)3 +(3b)3+3(2a)2(3b) + 3(2a)(3b)2
(2a+3b)3
(2a+3b) (2a+3b) (2a+3b)
Hence, 8a3+27b3+36a2b+54ab2 = (2a+3b) (2a+3b) (2a+3b)
问题9.分解8a 3 -27b 3 -36a 2 b + 54ab 2
解决方案：
As we know that, a3-b3-3a2b+3ab2 = (a-b)3
So, the above expression can be written as:
(2a)3 -(3b)3-3(2a)2(3b) + 3(2a)(3b)2
(2a-3b)3
(2a-3b) (2a-3b) (2a-3b)
Hence, 8a3-27b3-36a2b+54ab2 = (2a-3b) (2a-3b) (2a-3b)
问题10：分解x 3 – 12x(x-4)-64
解决方案：
As we know that, a3-b3-3a2b+3ab2 = (a-b)3
So, the above expression can be written as:
x3 -12x2 +48x -43
x3 -43-3(x)2(4) +3(x)(4)2
(x-4)3
(x-4) (x-4) (x-4)
Hence, x3 – 12x(x-4)-64 = (x-4) (x-4) (x-4)
问题11比化的3×3 -3a 2 BX 2 + 2 3AB XB 3
解决方案：
As we know that, a3-b3-3a2b+3ab2 = (a-b)3
So, the above expression can be written as:
(ax)3 -3(ax)2(b)+3(ax)(b)-b3
(ax-b)3
(ax-b) (ax-b) (ax-b)
Hence, a3x3 -3a2bx2 +3ab2x-b3 = (ax-b) (ax-b) (ax-b)