作业帮求解一道因式分解题
来源：学生作业帮助网 编辑：作业帮 时间：2024/10/05 16:08:36
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求解一道因式分解题
求解一道因式分解题
求解一道因式分解题
题是不是这样的：x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4 ?如果是的,
原式=x^4+2x^2y^2+y^4 + 5x^3y+5xy^3 + 6x^2y^2 + x^2y+xy^2
=(x^2+y^2)^2 + 5xy(x^2+y^2) + 6x^2y^2 + xy(x+y)
=(x^2+y^2)[(x^2+y^2)+5xy] + 6x^2y^2 - xy
=(x^2+y^2)[(x^2+y^2+2xy)+3xy] + 6x^2y^2 - xy
=(x^2+y^2)[(x+y)^2 + 3xy] + 6x^2y^2 - xy
=(x^2+y^2)(1+3xy) + 6x^2y^2 - xy
=(x^2+y^2) + 3xy(x^2+y^2) + 6x^2y^2 - xy
=(x^2+y^2) + 3xy[(x^2+y^2) + 2xy] - xy
=(x^2+y^2) + 3xy(x+y)^2 - xy
=(x^2+y^2) + 3xy - xy
=(x^2+y^2) + 2xy
=(x+y)^2
=1
选C
你好，轩辕酷剑神
题目应该是：
x^4+5x^3y+x^2y+8x^2y^2+xy^2+5xy^3+y^4
=(x+y)(x^3+4x^2y+xy+4xy^2+y^3)
=-[(x^3+y^3)+4xy(x+y)+xy]
=-(-x^2+xy-y^2-4xy+xy)
=x^2+2xy+y^2
=(x+y)^2
=(-1)²
=1
所以，选项C正确