把下列各多項式分解為因式：
1.(x-2)(x-1)3-(x-2)3(x-1)
2.a4-2a2b2+b4
中二數學題
2008-12-30 7:41 am
回答 (2)
2008-12-30 8:02 am
✔ 最佳答案
1.(x-2)(x-1)^3-(x-2)^3(x-1)
=(x-2)(x-1)[(x-1)^2-(x-2)^2]
=(x-2)(x-1)(x-1+x-2)(x-1-x+2)
=(x-2)(x-1)(2x-3)
2.
a^4-2a^2 b^2+b^4
=(a^2-b^2)^2
=[(a+b)(a-b)]^2
=(a+b)^2(a-b)^2
公式
x^2+2xy+y^2=(x+y)^2
x^2-y^2=(x+y)(x-y)
參考: me
2008-12-30 11:52 pm
1.
(x - 2)(x - 1)^3 - (x - 2)^3 (x - 1)
= (x - 2)(x - 1) [(x - 1)^2 - (x - 2)^2]......................抽(x - 2)(x - 1)出嚟
= (x - 2)(x - 1) [(x - 1) + (x - 2)][(x - 1) - (x - 2)]...a^2-b^2 = (a+b)(a-b)
= (x - 2)(x - 1)(x - 1 + x - 2)(x - 1 - x + 2)
= (x - 2)(x - 1)(x + x - 1 - 2)(x - x - 1 + 2 )
= (x - 2)(x - 1)(2x - 3)
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2.
a^4 - 2a^2 b^2 + b^4
= (a^2)^2 - 2(ab)^2 + (b^2)^2
= (a^2 - b^2)(a^2 - b^2)...................................a^2 - 2ab + b^2=(a-b)^2
= (a^2 - b^2)^2
(x - 2)(x - 1)^3 - (x - 2)^3 (x - 1)
= (x - 2)(x - 1) [(x - 1)^2 - (x - 2)^2]......................抽(x - 2)(x - 1)出嚟
= (x - 2)(x - 1) [(x - 1) + (x - 2)][(x - 1) - (x - 2)]...a^2-b^2 = (a+b)(a-b)
= (x - 2)(x - 1)(x - 1 + x - 2)(x - 1 - x + 2)
= (x - 2)(x - 1)(x + x - 1 - 2)(x - x - 1 + 2 )
= (x - 2)(x - 1)(2x - 3)
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2.
a^4 - 2a^2 b^2 + b^4
= (a^2)^2 - 2(ab)^2 + (b^2)^2
= (a^2 - b^2)(a^2 - b^2)...................................a^2 - 2ab + b^2=(a-b)^2
= (a^2 - b^2)^2
參考: me.
收錄日期: 2021-04-13 16:19:56
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