可以幫我因式分解這兩題嗎? (1)(x^2-y^2)^2-8(x^2+y^2)+16 (2)(2x+1)(x^2-x+3)+2x(x-6) ps:我要過程?

2017-01-27 8:15 pm

回答 (2)

2017-01-28 7:42 am
✔ 最佳答案
(1)(x^2-y^2)^2-8(x^2+y^2)+16
=(x^2-y^2)^2-8(x^2-y^2+2y^2)+16
=(x^2-y^2)^2-8(x^2-y^2)-16y^2+16
=(x^2-y^2)^2-8(x^2-y^2)+16-16y^2
=(x^2-y^2-4)^2-(4y)^2
=(x^2-y^2-4y-4)(x^2-y^2+4y-4)
=[x^2-(y+2)^2]*[x^2-(y-2)^2]
=(x-y-2)(x+y+2)(x-y+2)(x+y-2)
(2)(2x+1)(x^2-x+3)+2x(x-6)
=(2x^3-2x^2+6x+x^2-x+3)+(2x^2-12x)
=2x^3+x^2-7x+3
=(2x^3-x^2)+(2x^2-x)+(-6x+3)
=x^2(2x-1)+x(2x-1)-3(2x-1)
=(x^2+x-3)(2x-1)
2017-01-31 12:37 am
(1) (x²-y²)²-8(x²+y²)+16
=(x²-y²-4)(x²-y²-4)
(2)(2x+1)(x²-x+3)+2x(x-6)
=2x³-2x²+6x+x²-x+3+2x²-12x
=2x³+x²-7x+3
=2x³+x²-x-6x+3
=x(2x²+x-1)-3(2x-1)
=x(2x-1)(x+1)-3(2x-1)
=(2x-1)(x²+x-3)
算好久0.0請版主自己再確認是否有錯誤喔!!!希望能幫到你^^


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