因式分解下列各式:
(a) (3a+b)^2-(6a-b)^2
(b) (x-2y)^2-(2x-2y)^2
(c) (10x+3y)^2-(3x-10y)^2
(d) (x^2-6xy+9y^2)-x^4
數學問題!!!
2006-12-16 9:53 pm
回答 (3)
2006-12-16 10:09 pm
✔ 最佳答案
(a) (3a+b)^2-(6a-b)^2=(3a+b-6a+b)(3a+b+6a-b)
=9a(2b-3a)
(b) (x-2y)^2-(2x-2y)^2
=(x-2y-2x+2y)(x-2y+2x-2y)
=-x(3x-4y)
(c) (10x+3y)^2-(3x-10y)^2
=(10x+3y-3x+10y)(10x+3y+3x-10y)
=(7x+13y)(13X-7y)
(d) (x^2-6xy+9y^2)-x^4
=(x-3y)^2-x^4
=(x-3y-x^2)(x-3y+x^2)
參考: myself
2006-12-16 10:22 pm
(a)=(3a+b+6a-b)(3a+b-6a+b)
=(9a)(-3a+2b)
=18ab-27a^2......(formula:a^2-b^2=(a+b)(a-b))
(b)=(x-2y+2x-2y)(x-2y-2x+2y)
=(3x-4y)(-x)
=4xy-3x^2
(c)=(10x+3y+3x-10y)(10x+3y-3x+10y)
=(13x-7y)(7x+13y)
=91x^2+169xy-49x^2-91y^2
=42x^2+169xy-91y^2
(d)=(x-3y)^2-x^4......formula:(a-b)^2=a^2-2ab+b^2
/=(x-3y+x^2)(x-3y-x^2)
=(9a)(-3a+2b)
=18ab-27a^2......(formula:a^2-b^2=(a+b)(a-b))
(b)=(x-2y+2x-2y)(x-2y-2x+2y)
=(3x-4y)(-x)
=4xy-3x^2
(c)=(10x+3y+3x-10y)(10x+3y-3x+10y)
=(13x-7y)(7x+13y)
=91x^2+169xy-49x^2-91y^2
=42x^2+169xy-91y^2
(d)=(x-3y)^2-x^4......formula:(a-b)^2=a^2-2ab+b^2
/=(x-3y+x^2)(x-3y-x^2)
參考: myself
2006-12-16 9:58 pm
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收錄日期: 2021-04-13 17:13:36
原文連結 [永久失效]:
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