把下列各式分解因式1.(a+1)
(1)
(a+1)^2-(a^2+a)^2
=(a+1)^2-a^2(a+1)^2
=(a+1)^2(1-a^2)
=(a+1)^2(1+a)(1-a)
=(1-a)(1+a)^3。
(2)
(x+y)^3-9(x+y)^2
=(x+y)^2(x+y-9)
(3)
4-12(x-y)+9(x-y)^2
=[3(x-y)]^2-2×2×3(x-y)+2^2
=[3(x-y)-2]^2
=(3x-3y-2)^2。
(4)
(1/4)a^2+(1/3)ab+(1/9)b^2
=(a/2)^2+2×(a/2)×(b/3)+(b/3)^2
=(a/2-b/3)^2
=(1/36)(3a-2b...全部
(1)
(a+1)^2-(a^2+a)^2
=(a+1)^2-a^2(a+1)^2
=(a+1)^2(1-a^2)
=(a+1)^2(1+a)(1-a)
=(1-a)(1+a)^3。
(2)
(x+y)^3-9(x+y)^2
=(x+y)^2(x+y-9)
(3)
4-12(x-y)+9(x-y)^2
=[3(x-y)]^2-2×2×3(x-y)+2^2
=[3(x-y)-2]^2
=(3x-3y-2)^2。
(4)
(1/4)a^2+(1/3)ab+(1/9)b^2
=(a/2)^2+2×(a/2)×(b/3)+(b/3)^2
=(a/2-b/3)^2
=(1/36)(3a-2b)^2。
(5)
7x^(n+1)-14x^n+7x^(n-1)
=7x^(n-1)·(x^2-2x+1)
=7x^(n-1)·(x-1)^2。
(6)
(x+2)(x+3)+x^2-4
=(x+2)(x+3)+(x+2)(x-2)
=(x+2)[(x+3)+(x-2)]
=(x+2)(2x+1)。
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