分解因式 平方差公式法

(1)a^n-1-4a^n+1

(2)1/7(x-y)^3+7(y-x)

(3)(2a-b+c)^2-(3a+2b-c)^2

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

(1)a^n-1-4a^n+1 =A^N-1(1-4A方)=A^N-1(1+2A)(1-2A)

(2)1/7(x-y)^3+7(y-x) =(X-Y)/7*[(X-Y)方-49]=(X-Y)/7*(X-Y+7)(X-Y-7)

(3)(2a-b+c)^2-(3a+2b-c)^2 =(2A-B+C+3A+2B-C)(2A-B+C-3A-2B+C)
=(5A+B)(-A-3B+2C)

(4)4x^3-8x^2y-xy^2+2y^3
=4X立-XY方-(8X方Y-2Y立)
=X(4X方-Y方)-2Y(4X方-Y方)
=(X-2Y)(2X+Y)(2X-Y)

(1-1/5的平方)(1-1/6的平方)...(1-1/2009的平方)

=(1-1/5^2)(1-1/6^2)...(1-1/2009^2)

=(1-1/5)......(1-1/2009) *(1+1/5)...(1+1/2009)

=(4/5)(5/6)...(2008/2009) *(6/5)(7/6)...(2010/2009)

=(4/2009)(2010/5)

=1608/2009

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