解下列因式分解(1)x^2+12x+36(2)-2xy-x^2-y^2(3)a^2+2a+1(4)4x^2-4x+1(5
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解下列因式分解
(1)x^2+12x+36
(2)-2xy-x^2-y^2
(3)a^2+2a+1
(4)4x^2-4x+1
(5)ax^2+2a^2x+a^3
(6)-3x^2+6xy-3y^2
(1)x^2+12x+36
(2)-2xy-x^2-y^2
(3)a^2+2a+1
(4)4x^2-4x+1
(5)ax^2+2a^2x+a^3
(6)-3x^2+6xy-3y^2
解
x²+12x+36
=x²+2×6x+6²
=(x+6)²
-2xy-x²-y²
=-(x²+2xy+y²)
=-(x+y)²
a²+2a+1
=(a+1)²
4x²-4x+1
=(2x)²-2×2x+1²
=(2x-1)²
ax²+2a²x+a³
=a(x²+2ax+a²)
=a(x+a)²
-3x²+6xy-3y²
=-3(x²-2xy+y²)
=-3(x-y)²
都是用到完全平方公式
x²+12x+36
=x²+2×6x+6²
=(x+6)²
-2xy-x²-y²
=-(x²+2xy+y²)
=-(x+y)²
a²+2a+1
=(a+1)²
4x²-4x+1
=(2x)²-2×2x+1²
=(2x-1)²
ax²+2a²x+a³
=a(x²+2ax+a²)
=a(x+a)²
-3x²+6xy-3y²
=-3(x²-2xy+y²)
=-3(x-y)²
都是用到完全平方公式
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