數學 f.2 factorization

1.6^3 - (4+3x)^3
=[6-(4+3x)][6^2+(6)(4+3x)+(4+3x)^2]
=(2-3x)[36+(24+18x)+(16+24x+9x^2)]
=(2-3x)(76+42x+9x^2)

2.(2x)^3 + (2-x)^3
=[2x+(2-x)][(2x)^2-(2x)(2-x)+(2-x)^2]
=(2+x)[4x^2-(4x-2x^2)+(x^2-4x+4)]
=(2+x)(7x^2-8x+4)

3.125x^3 - (x+y)^3
=(5x)^3-(x+y)^3
=[5x-(x+y)][(5x)^2+(5x)(x+y)+(x+y)^2]
=(4x+y)[25x^2+(5x^2+5xy)+(x^2+2xy+y^2)]
=(4x+y)(31x^2+7xy+y^2)

4.(5a-6)^3 +729
=(5a-6)^3+(9)^3
=[(5a-6)+9][(5a-6)^2-(5a-6)(9)+(9)^2]
=(5a+3)[(25a^2-60a+36)-(45a-54)+81]
=(5a+3)(25a^2-105a+171)

可以用公式
a³ - b³ = (a-b) (a² +ab+ b²)
a³ + b³ = (a+b) (a² -ab+ b²)


1.6^3 - (4+3x)^3
=6³ -(4+3x)³
=[6-(4+3x)] [6² +6(4+3x)+ (4+3x)²]
=(6-4-3x)(36 +24+18x +16+24x+9x²)
=(2-3x)(76+42x+9x²)


2.(2x)^3 + (2-x)^3
=(2x)³ + (2-x)³
=[2x+(2-x)][(2x)²-(2x)(2-x)+(2-x)²]
=(2x+2-x)(4x² -4x+2x² +4-4x+x²)
=(x+2)(7x²-8x+4)


3.125x^3 - (x+y)^3
=(5x)³ -(x+y)³
=[5x-(x+y)][(5x)²+(5x)(x+y)+(x+y)²]
=(5x-x-y)(25x² +5x²+5xy +x²+2xy+y²)
=(4x-y)(31x²+7xy+y²)


4.(5a-6)^3 +729
=(5a-6)³ +9³
=[(5a-6)+9] [(5a-6)² -9(5a-6) +9²]
=(5a-6+9)(25a²-60a+36 -45a+54 +81)
=(5a+3) (25a²-105a+171)

2008-11-23 13:50:03 補充：
002
3. 錯左 0.0

1)152-144x-108x^2-27x^3
2)8-12x-6x^2+7x^3
3)124x^3-3(x^2)y-3xy^2-y^3
4)81+540a-450a^2+125a^3

2008-11-23 12:32:10 補充：
2)8-12x+6x^2+7x^3