Question

因式分解

一ab(c^2+d^2)+cd(a^2+b^2)
二3a^2x^2-15a^2xy-42a^2y^2
三a^3b-3a^2b+6ab-18b
四4a-1+b^2-4a^2
五(a^2-1)(a^2+8a+15)-20
六a^2-b^2+2bc-c^2
七2a^3-2a^2b+8b-8a
八3x^3+6x^2y-3x^2-6xy

Answer 1

一ab(c^2+d^2)+cd(a^2+b^2)
=abc²+abd²+a²cd+b²cd
=abc²+a²cd+abd²+b²cd
=ac(bc+ad)+bd(ad+bc)
=(bc+ad)(ac+bd)

二3a^2x^2-15a^2xy-42a^2y^2
=3a²(x²-5xy-14y²)
=3a²(x-7y)(x+2y)

三a^3b-3a^2b+6ab-18b
=a²b(a-3)+6b(a-3)
=b(a-3)(a²+6)

四4a-1+b^2-4a^2
=b²-4a²+4a-1
=b²-(2a-1)²
=(b+2a-1)(b-2a+1)

五(a^2-1)(a^2+8a+15)-20
=(a-1)(a+1)(a+3)(a+5)-20
=(a-1)(a+5)(a+1)(a+3)-20
=(a²+4a-5)(a²+4a+3)-20
=(a²+4a)²-2(a²+4a)-35
=(a²+4a-7)(a²+4a+5)

六a^2-b^2+2bc-c^2
=a²-(b²-2bc+c²)
=a²-(b-c)²
=(a+b-c)(a-b+c)

七2a^3-2a^2b+8b-8a
=2a²(a-b)-8(a-b)
=2(a-b)(a²-4)
=2(a-b)(a+2)(a-2)

八3x^3+6x^2y-3x^2-6xy
=3x²(x+2y)-3x(x+2y)
=3x(x+2y)(x-1)

Answer 2

1.（ad+bc）(ac+bd)
2.(a^2x-7a^2y)(3x+6y)

Answer 3

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