①2x²-5xy-12y²+8x+y+6②x³+2x-12③x的5次方-x²-28④x³+y³+z³-3xyz
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![①2x²-5xy-12y²+8x+y+6②x³+2x-12③x的5次方-x²-28④x³+y³+z³-3xyz](/uploads/image/z/5621527-55-7.jpg?t=%E2%91%A02x%26%23178%3B%EF%BC%8D5xy%EF%BC%8D12y%26%23178%3B%EF%BC%8B8x%EF%BC%8By%EF%BC%8B6%E2%91%A1x%26%23179%3B%EF%BC%8B2x%EF%BC%8D12%E2%91%A2x%E7%9A%845%E6%AC%A1%E6%96%B9%EF%BC%8Dx%26%23178%3B%EF%BC%8D28%E2%91%A3x%26%23179%3B%EF%BC%8By%26%23179%3B%EF%BC%8Bz%26%23179%3B%EF%BC%8D3xyz)
①2x²-5xy-12y²+8x+y+6②x³+2x-12③x的5次方-x²-28④x³+y³+z³-3xyz
①2x²-5xy-12y²+8x+y+6
②x³+2x-12
③x的5次方-x²-28
④x³+y³+z³-3xyz
①2x²-5xy-12y²+8x+y+6②x³+2x-12③x的5次方-x²-28④x³+y³+z³-3xyz
1、(2x+3y)(x-4y)+8x+y+6
=(2x+3y+2)(x-4y+3)
2、x³-2x²+2x²-4x+6x-12
=x²(x-2)+2x(x-2)+6(x-2)
=(x-2)(x²+2x+6)
3、x的5次方-2x的4次方+2x的4次方-4x³+4x³-8x²+7x²-14x+14x-18
=x的4次方(x-2)+2x³(x-2)+4x²(x-2)+7x(x-2)+14(x-2)
=(x-2)(x的4次方+2x³+4x²+7x+14)
4、
x³+y³+z³-3xyz
= (x³+3yx²+3xy²+y³)+z³-3xyz-3yx²-3xy²
= (x+y)³+z³-3xy(x+y+z)
= (x+y+z)[(x+y)²-(x+y)z+z²]-3xy(x+y+z)
= (x+y+z)[(x²+2xy+y²-xz-yz+z²)-2xy]
= (x+y+z)(x²+y²+z²-xy-yz-zx)
2x^2-5xy-12y^2+8x+y+6
=(x-4y)(2x+3y)+8x+y+6
=(x-4y+3)(2x+3y+2)
x^2+2x-12
=(x-2)(x^2+2x+6)
x的5次方-x^2-28
=(x-2)(x^4+2x^3+4x^2+7x+14)
x^3+y^3+z^3-3xyz
= (x^3+3yx^2+3xy^2+...
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2x^2-5xy-12y^2+8x+y+6
=(x-4y)(2x+3y)+8x+y+6
=(x-4y+3)(2x+3y+2)
x^2+2x-12
=(x-2)(x^2+2x+6)
x的5次方-x^2-28
=(x-2)(x^4+2x^3+4x^2+7x+14)
x^3+y^3+z^3-3xyz
= (x^3+3yx^2+3xy^2+y^3)+z^3-3xyz-3yx^2-3xy^2
= (x+y)^3+z^3-3xy(x+y+z)
= (x+y+z)[(x+y)^2-(x+y)z+z^2]-3xy(x+y+z)
= (x+y+z)[(x^2+2xy+y^2-xz-yz+z^2)-2xy]
= (x+y+z)(x^2+y^2+z^2-xy-yz-zx)
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