因式分解 4x^2-12xy+12xz+(y-z)^2 请高手回答一下。类似的题目也行。
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4x²-12xy+12xz+(y-z)²
=4x²-12x(y-z)+(y-z)²
=4x²-12x(y-z)+9(y-z)²-8(y-z)²
=[2x+3(y-z)]²-8(y-z)²
=[2x+3(y-z)+2√2(y-z)][2x+3(y-z)-2√2(y-z)]
=[2x+(3+2√2)(y-z)][2x+(3-2√2)(y-z)]
=4x²-12x(y-z)+(y-z)²
=4x²-12x(y-z)+9(y-z)²-8(y-z)²
=[2x+3(y-z)]²-8(y-z)²
=[2x+3(y-z)+2√2(y-z)][2x+3(y-z)-2√2(y-z)]
=[2x+(3+2√2)(y-z)][2x+(3-2√2)(y-z)]
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