作业帮因式分解:1.x5+x4+12 2.(ax+by)2+(bx-ay)2 3.x3-3x2+4 4.(x+y)2-4(x+y-1) 5.p的m+3次方-p的m次方6.3x4-7x2y2+3y4 7.ab(c2+d2）+cd(a2+b2)第一题打错了，应该是x5+x4+1
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因式分解:1.x5+x4+12 2.(ax+by)2+(bx-ay)2 3.x3-3x2+4 4.(x+y)2-4(x+y-1) 5.p的m+3次方-p的m次方6.3x4-7x2y2+3y4 7.ab(c2+d2）+cd(a2+b2)第一题打错了，应该是x5+x4+1
因式分解:1.x5+x4+12 2.(ax+by)2+(bx-ay)2 3.x3-3x2+4 4.(x+y)2-4(x+y-1) 5.p的m+3次方-p的m次方
6.3x4-7x2y2+3y4 7.ab(c2+d2）+cd(a2+b2)
第一题打错了，应该是x5+x4+1
因式分解:1.x5+x4+12 2.(ax+by)2+(bx-ay)2 3.x3-3x2+4 4.(x+y)2-4(x+y-1) 5.p的m+3次方-p的m次方6.3x4-7x2y2+3y4 7.ab(c2+d2）+cd(a2+b2)第一题打错了，应该是x5+x4+1
1.x5+x4+1
=x^5-x^3+x^4-x^2+x^3+x^2-x+x+1
=x^3(x^2-1)+x^2(x^2-1)+x(x^2-1)+x^2+x+1
=(x^2-1)(x^3+x^2+x)+(x^2+x+1)
=x(x^2-1)(x^2+x+1)+(x^2+x+1)
=(x^2+x+1)(x^3-x+1)
2.(ax+by)^2+(bx-ay)^2
=(ax)^2+(by)^2+(bx)^2+(ay)^2
= a^2(x^2+y^2)+b^2(x^2+y^2)
=(x^2+y^2)(a^2+b^2)
3.x^3-3x^2+4
=x^3-2x^2-x^2+4
=x^2(x-2)-(x+2)(x-2)
=(x-2)(x^2-x-2)
=(x-2)^2(x+1)
4.(x+y)^2-4(x+y-1)
=(x+y)^2-4(x+y)+4
=(x+y-2)^2
5.p^(m+3)-p^m
=p^m(p^3-1)
=p^m(p-1)(p^2+p+1)
6.3x^4-7x^2^y2+3y^4
=3x^4-6x^2y^2+3y^4-x^2y^2
=3(x^2-y^2)^2-x^2y^2
= （√3x^2-√3y^2+xy)(√3x^2-√3y^2-xy)
7.ab(c^2+d^2）+cd(a^2+b^2)
=abc^2+abd^2+a^2cd+b^2cd
=ac(bc+ad)+bd(ad+bc)
=(bc+ad)(ac+bd)
1：X5+X4+1=X（5+4）+1
2：(ax+by)2+(bx-ay)2=(ax+by+bx-ay)2=(a(x-y)+b(x+y))2
3:x3-3x2+4=3x-6x+4=x(3-6)+4=-3x+4
4:(x+y)2-4(x+y-1)=(x+y)2-(x+y)4-4=-2(x+y)-4=-(2(x+y)-4)
5:
6:=12x-28xy+12y=12(x+y)-28xy
7:=2ab(c+d)+2cd(a+b)=2(abc+abd+acd+bcd)