X∧4+4Y∧4X∧3-3X∧2-2X+216X∧2-9Y∧2+32X+16X∧4+X∧2Y∧2+Y∧4
来源:学生作业帮 编辑:大师作文网作业帮 分类:数学作业 时间:2024/09/22 15:29:24
X∧4+4Y∧4
X∧3-3X∧2-2X+2
16X∧2-9Y∧2+32X+16
X∧4+X∧2Y∧2+Y∧4
X∧3-3X∧2-2X+2
16X∧2-9Y∧2+32X+16
X∧4+X∧2Y∧2+Y∧4
x^4+4y^4
=x^4+4y^4+4x²y²-4x²y²
=(x²+2y²)²-4x²y²
=(x²+2y²+2xy)(x²+2y²-2xy)
X³-3X²-2X+2
=(x³+1)-(3x²+2x-1)
=(x+1)(x²-x+1)-(x+1)(3x-1)
=(x+1)(x²-x+1-3x+1)
=(x+1)(x²-4x+2)
16X²-9Y²+32X+16
=(4x+4)²-9y²
=(4x+4-3y)(4x+4+3y)
X^4+X²Y²+Y^4
=x^4+y^4+2x²y²-x²y²
=(x²+y²)²-x²y²
=(x²+y²+xy)(x²+y²-xy)
=x^4+4y^4+4x²y²-4x²y²
=(x²+2y²)²-4x²y²
=(x²+2y²+2xy)(x²+2y²-2xy)
X³-3X²-2X+2
=(x³+1)-(3x²+2x-1)
=(x+1)(x²-x+1)-(x+1)(3x-1)
=(x+1)(x²-x+1-3x+1)
=(x+1)(x²-4x+2)
16X²-9Y²+32X+16
=(4x+4)²-9y²
=(4x+4-3y)(4x+4+3y)
X^4+X²Y²+Y^4
=x^4+y^4+2x²y²-x²y²
=(x²+y²)²-x²y²
=(x²+y²+xy)(x²+y²-xy)
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