求几题解法,(因式分解)急~1.(x²+4x+3)(x²+12x+35)+152.(a²+19a)²-408(a²+19a0-1248483.(ab-1)²+(a+b-2)(a+b-2ab)4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)
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![求几题解法,(因式分解)急~1.(x²+4x+3)(x²+12x+35)+152.(a²+19a)²-408(a²+19a0-1248483.(ab-1)²+(a+b-2)(a+b-2ab)4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)](/uploads/image/z/4329799-7-9.jpg?t=%E6%B1%82%E5%87%A0%E9%A2%98%E8%A7%A3%E6%B3%95%2C%EF%BC%88%E5%9B%A0%E5%BC%8F%E5%88%86%E8%A7%A3%EF%BC%89%E6%80%A5%7E1.%28x%26sup2%3B%2B4x%2B3%EF%BC%89%EF%BC%88x%26sup2%3B%2B12x%2B35%EF%BC%89%2B152.%EF%BC%88a%26sup2%3B%2B19a%EF%BC%89%26sup2%3B-408%EF%BC%88a%26sup2%3B%2B19a0-1248483.%28ab-1%29%26sup2%3B%2B%EF%BC%88a%2Bb-2%EF%BC%89%EF%BC%88a%2Bb-2ab%EF%BC%894.xy%EF%BC%88x%26sup2%3B-y%26sup2%3B%EF%BC%89%2Byz%EF%BC%88y%26sup2%3B-z%26sup2%3B%EF%BC%89%2Bzx%EF%BC%88z%26sup2%3B-x%26sup2%3B%EF%BC%89)
求几题解法,(因式分解)急~1.(x²+4x+3)(x²+12x+35)+152.(a²+19a)²-408(a²+19a0-1248483.(ab-1)²+(a+b-2)(a+b-2ab)4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)
求几题解法,(因式分解)急~
1.(x²+4x+3)(x²+12x+35)+15
2.(a²+19a)²-408(a²+19a0-124848
3.(ab-1)²+(a+b-2)(a+b-2ab)
4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)
求几题解法,(因式分解)急~1.(x²+4x+3)(x²+12x+35)+152.(a²+19a)²-408(a²+19a0-1248483.(ab-1)²+(a+b-2)(a+b-2ab)4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)
1.原式=(x+3)(x+1)(x+5)(x+7)+15
=(x+1)(x+7)(x+3)(x+5)+15
=(x^2+8x+7)(x^2+8x+15)+15
=(x^2+8x+7)^2+8(x^2+8x+7)+15
=(x^2+8x+7+5)(x^2+8x+7+3)
=(x^2+8x+12)(x^2+8x+10)
=(x+2)(x+6)(x^2+8x+10)
2.原式=(a^2+19a)^2-408(a^2+19a)-124848
=(a^2+19a)^2-24*17(a^2+19a)-36*17*12*17
=(a^2+19a-36*17)(a^2+19a+12*17)
=(a-17)(a+36)(a^2+19a+204)
3.取ab=A,a+b=B
则原式=(A-1)^2+(B-2)(B-2A)
=A^2-2A+1+B^2-2AB-2B+4A
=A^2-2(B-1)A+B^2-2B+1
=A^2-2(B-1)A+(B-1)^2
=(A-B+1)^2
=(ab-a-b+1)^2
=(a-1)^2(b-1)^2
4.原式=yx^3-xy^3+zy^3-yz^3+xz^3-zx^3
=(y-z)x^3+(z-y)(z^2+y^2+zy)x+zy(y-z)(y+z)
=(y-z)(x^3-(z^2+y^2+yz)x+zy(y+z))
=(y-z)(x^3+(y+z)x^2-(y+z)x^2-(y^2+z^2+yz)x+yz(y+z))
=(y-z)(x^2(x+y+z)-(x+y+z)((y+z)x-zy))
=(y-z)(x+y+z)(x^2-(y+z)x+zy)
=(y-z)(x+y+z)(x-z)(x-y)
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4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)=yx^3-xy^3+zy^3-yz^3+xz^3-zx^3
=(y-z)x^3+(z-y)(z^2+y^2+zy)x+zy(y-z)(y+z)
=(y-z)(x^3-(z^2+y^2+yz)x+zy(y+z))
=(y-z)(x^3+(y+z)x^2-...
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4.xy(x²-y²)+yz(y²-z²)+zx(z²-x²)=yx^3-xy^3+zy^3-yz^3+xz^3-zx^3
=(y-z)x^3+(z-y)(z^2+y^2+zy)x+zy(y-z)(y+z)
=(y-z)(x^3-(z^2+y^2+yz)x+zy(y+z))
=(y-z)(x^3+(y+z)x^2-(y+z)x^2-(y^2+z^2+yz)x+yz(y+z))
=(y-z)(x^2(x+y+z)-(x+y+z)((y+z)x-zy))
=(y-z)(x+y+z)(x^2-(y+z)x+zy)
=(y-z)(x+y+z)(x-z)(x-y)
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