因式分解拔高题(1)ac-bc+a^2-b^2=(2)3(x-y)m^3+27(y-x)m=(3)(y^2-1)(y+3)(y+5)-9=(4)(x+1)(x+2)(x+3)(x+4)-1=

Question

因式分解拔高题
(1)ac-bc+a^2-b^2=
(2)3(x-y)m^3+27(y-x)m=
(3)(y^2-1)(y+3)(y+5)-9=
(4)(x+1)(x+2)(x+3)(x+4)-1=

Answer 1

(1)ac-bc+a^2-b^2
=c(a－b)＋(a＋b)(a－b)
=(a＋b＋c)(a－b)
(2)3(x-y)m^3+27(y-x)m
=3(x－y)m^3－27(x－y)m
=3(x－y)m(m²－9)
=3(x－y)m(m＋3)(m－3)
(3)(y^2-1)(y+3)(y+5)-9
=(y＋1)(y＋3)(y－1)(y＋5)－9
=(y²＋4y＋3)(y²＋4y－5)－9
=(y²＋4y)²－2(y²＋4y)－15－9
=(y²＋4y)²－2(y²＋4y)－24
=(y²＋4y－6)(y²＋4y＋4)
=(y²＋4y－6)(y＋2)²
(4)(x+1)(x+2)(x+3)(x+4)-1
此题有误吧!
应该是(x+1)(x+2)(x+3)(x+4)＋1
=(x+1)(x+4)(x+2)(x+3)＋1
=(x²＋5x＋4)(x²＋5x＋6)＋1
=(x²＋5x)²＋10(x²＋5x)＋24＋1
=(x²＋5x)²＋10(x²＋5x)＋25
=(x²＋5x＋5)²