Question

数学题解答！！！！！！！！！！跪求！！！！！！！！！

因式分解：①x³-1②（x+y)的四次方-(x-y)的四次方
③x²y²-y的四次方-12xy²+36y²

Answer 1

因式分解：
①x³-1
=(x-1)(x^2+x+1)

②（x+y)的四次方-(x-y)的四次方
=[(x+y)²+(x-y)²]*[(x+y)²-(x-y)²]
=(2x²+2y²)(4xy)
=8xy(x²+y²)
③x²y²-y的四次方-12xy²+36y²
=y²(x²-y²-12x+36)

追问

第一个是怎么做的呢

追答

直接运用立方差公式：
a^3-b^3=(a-b)(a^2+ab+b^2)

追问

第三个呢，过程！！！！！

Answer 2

①x³-1
原式=(x-1)(x²+x+1)
②（x+y)的四次方-(x-y)的四次方
原式=[(x+y)²+(x-y)²][(x+y)²-(x-y)²]
=[(x+y)²+(x-y)²][(x+y)-(x-y)][(x+y)+(x-y)]
=[(x+y)²+(x-y)²](x+y-x+y)(x+y+x-y)
=[(x+y)²+(x-y)²]*2y*2x
=4xy[(x+y)²+(x-y)²]
=4xy(x²+2xy+y²+x²-2xy+y²)
=8xy(x²+y²)
③x²y²-y的四次方-12xy²+36y²
原式=y²(x²-y²-12x+36)
=y²[(x²-12x+36)-y²]
=y²[(x-6)²-y²]
=y²(x+y-6)(x-y-6)

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追问

第一个是怎么做的呢

Answer 3

①x³-1
原式=(x-1)(x²+x+1)
②（x+y)的四次方-(x-y)的四次方
原式=[(x+y)²+(x-y)²][(x+y)²-(x-y)²]
=[(x+y)²+(x-y)²][(x+y)-(x-y)][(x+y)+(x-y)]
=[(x+y)²+(x-y)²](x+y-x+y)(x+y+x-y)
=[(x+y)²+(x-y)²]*2y*2x
=4xy[(x+y)²+(x-y)²]
=4xy(x²+2xy+y²+x²-2xy+y²)
=8xy(x²+y²)
③x²y²-y的四次方-12xy²+36y²
原式=y²(x²-y²-12x+36)
=y²[(x²-12x+36)-y²]
=y²[(x-6)²-y²]
=y²(x+y-6)(x-y-6)

Answer 4

1.x^3-1=(x-1)(x^2+x+1)

2.(x+y)^4-(x-y)^4
=[(x+y)^2+(x-y)^2][(x+y)^2-(x-y)^2]
=(x^2+2xy+y^2+x^2-2xy+y^2)(x+y+x-y)(x+y-x+y)
=2(x^2+y^2)*4xy
=8xy(x^2+y^2)
3.x^2y^2-y^4-12xy^2+36y^2
=y^2[(x^2-12x+36)-y^2]
=y^2[(x-6)^2-y^2]
=y^2(x-6+y)(x-6-y)

Answer 5

1.（x-1)*(x^2+x+1)2.