因式分解4x²+4xy-y²4x²+4xy-y² ,答案是[2x+(1+√2)y][2x+(1-√2)y]为什么

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因式分解4x²+4xy-y²4x²+4xy-y² ,答案是[2x+(1+√2)y][2x+(1-√2)y]为什么
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因式分解4x²+4xy-y²4x²+4xy-y² ,答案是[2x+(1+√2)y][2x+(1-√2)y]为什么
因式分解4x²+4xy-y²
4x²+4xy-y² ,答案是[2x+(1+√2)y][2x+(1-√2)y]为什么

因式分解4x²+4xy-y²4x²+4xy-y² ,答案是[2x+(1+√2)y][2x+(1-√2)y]为什么
4x²+4xy-y²
=4x²+4xy+y² -2y²
=(2x+y)² -2y²
=(2x+y+√2y)(2x+y-√2y)
=[2x+(1+√2)y][2x+(1-√2)y]
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4X²+4XY-Y²
=4X²+4XY+Y² -2Y²
=(2X+Y)²-2Y²
=(2X+Y)² -(√2y)²
=[2x+(1+√2)y][2x+(1-√2)y]

这是典型的十字相乘法吧。。
4x² 4xy -y²
2x*2x 4 (1+√2)*(1-√2)
2*(1+√2)+2*(1-√2)=4
so 分解为
[2x+(1+√2)y][2x+(1-√2)y]