中三Math Question

方法一：

使用公式: (a + b)3 = a3 + 3a2b + 3ab2 + b3

(x + 4)3 - x3

= (x3 + 3[4]x2 + 3[4]2x + 43) - x3

= (x3 + 12x2 + 48x + 64) - x3

= x3 + 12x2 + 48x + 64 - x3

= 12x2 + 48x + 64

= 4(3x2) + 4(12x) + 4(16)

= 4(3x2 + 12x + 16)

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方法二：

使用公式: a3 - b3 = (a - b)(a2 + ab + b2)

及 (a + b)2 = a2 + 2ab + b2

設 a = (x + 4) 及 b = x

(x + 4)3 - x3

= a3 - b3

= {a - b}{a2 + ab + b2}

= {[x + 4] - x}{[x + 4]2 + [x + 4]x + x2}

= {x + 4 - x}{[x2 + 2x(4) + (4)2] + [x2 + 4x] + x2}

= 4{x2 + 8x + 16 + x2 + 4x + x2}

= 4(x2 + x2 + x2 + 8x + 4x + 16)

= 4(3x2 + 12x + 16)

=

(x+4)3-x3
(Remember the formula: x3-y3=(x-y)(x2+xy+y2) )
= (x+4-x)(x2+8x+16+x2+4x+x2)
=4(3x2+12x+16)


2008-10-27 21:29:07 補充：
Other formula:

x^3+y^3=(x+y)(x^2-xy+y^2)