Question

x^2y^4-x^4y^2

公式法因式分解

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Answer 1

x^2y^4-x^4y^2
=x^2y^2(y^2-x^2)
=x^2y^2(y+x)(y-x)

追问

(x+y)(5m+3n)^2-(x+y)(m-n)^2
m^2(m-n)+n^2(n-m)
(a-b)(3a+b)^2+(a+3b)^2(b-a)
(x+y)^4-(x-y)^4
(x^2+y^2)^2-4x^2y^2
198^2-202^2
675^2×31-575^2×31

追答

(x+y)(5m+3n)^2-(x+y)(m-n)^2=(x+y)[(5m+3n)^2-(m-n)^2]
=(x+y)[(5m+3n)+(m-n)][(5m+3n)-(m-n)]
=(x+y)[6m+2n][4m+4n]
=8(x+y)(3m+n)(m+n)
m^2(m-n)+n^2(n-m)=(m-n)(m^2-n^2)
=(m-n)(m+n)(m-n)
=(m+n)(m-n)^2
(a-b)(3a+b)^2+(a+3b)^2(b-a)=(a-b)[(3a+b)^2-(a+3b)^2]
=(a-b)[(3a+b)+(a+3b)][(3a+b)-(a+3b)]
=(a-b)[4a+4b][2a-2b]
=8(a+b)(a-b)^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)]
=(2x^2+2y^2)[2x][2y]
=8xy(x^2+y^2)
(x^2+y^2)^2-4x^2y^2=(x^2+y^2+2xy)(x^2+y^2-2xy)
=(x+y)^2(x-y)^2
198^2-202^2=(198+202)(198-202)
=400×(-4)
=-1600
675^2×31-575^2×31=31×(675^2-575^2)
=31×(675+575)(675-575)
=31×1250×100
=3875000

追问

O(∩_∩)O哈！你还真答了！
好吧好吧，你厉害……

Answer 2

答案如下
x^2y^4-x^4y^2
=x^2y^2(y^2-x^2)
=x^2y^2(y+x)(y-x)

追问

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