兩條數學問題,3次方

(1) a^3 + b^3 = (a+b)(a^2 -ab +b^2 )
(2) a^3 - b^3 = (a-b)(a^2 +ab +b^2 )


1. -343-8y^3
= -8y^3-343
= -(8y^3+343)
= -[ (2y)^3 + 7^3 ]
= -(2y+7)[ (2y)^2 -(2y)(7) +7^2 ] ->用(1)
= -(2y+7)(4y^2-14y+14) ->抽個2出黎
= -2(2y+7)(2y^2-7y+7)

2. (x+y)^3-8(x-y)^3
= (x+y)^3-[2(x-y)]^3
= [x+y-2(x-y)] {(x+y)^2 +(x+y)[2(x-y)] +[2(x-y)]^2 } ->用(2)
= (x+y-2x+2y) [x^2 +2xy +y^2 +(x+y)(2)(x-y) +(2)^2(x-y)^2]
= (-x+3y) [x^2 +2xy +y^2 +2(x^2 -y^2) +4(x^2 -2xy +y^2)] ->前面抽個負出黎
= -(x-3y) (x^2 +2xy +y^2 +2x^2 -2y^2 +4x^2 -8xy +4y^2)
= -(x-3y) (7x^2 -6xy +3y^2)

2012-07-24 18:46:57 補充：
1. -343-8y^3
= -8y^3-343
= -(8y^3+343)
= -[ (2y)^3 + 7^3 ]
= -(2y+7)[ (2y)^2 -(2y)(7) +7^2 ] ->用(1)
= -(2y+7)(4y^2-14y+49) ->呢到錯左 sorry

1. -343-8y^3
= -7^3 - (2y)^3
= -(7^3 + (2y)^3)
= -(7 + 2y)(7^2 - 7(2y) + (2y)^2)
= -(7 + 2y)(49 - 14y + 4y^2)

2 (x+y)^3-8(x-y)^3
= (x + y)^3 - [2(x - y)^3]
= (x + y - [2(x - y)]) {(x + y)^2 + (x + y) [2(x - y)] + [2(x - y)]^2}
= (3y - x)(7x^2 - 2xy + 3y^2)

1.
-343-8y^3
=-(343+8y^3)
=-(7+2y)(49-14y+4y^2)

2
(x+y)^3-8(x-y)^3
=[(x+y)-(x-y)][(x+y)^2+2(x+y)(x-y)+(x-y)^2]
=y[x^2+2xy+y^2+2(x^2-y^2)+x^2-2xy+y^2]
=y(2x^2+2y^2+2x^2-2y^2)
=y(4x^2)