Factor completely: 9x³y² - 36x Factor by grouping: 6x - 6y - 5ax + 5ay?
回答 (8)
2008-10-15 2:52 pm
✔ 最佳答案
(6-5a)(x-y).
2008-10-11 4:28 pm
Factor 9x out of both terms
9x(x^2y^2 - 4)
The second is the difference to two squares
(a^2 - b^2) (a+b)(a-b)
9x(xy+2)(xy-2)
Factor 6 out of the first two terms
6(x-y)
Factor -5a out of the third and fourth
-5a(x - y)
Since there is the common factor of (x-y)
(6 - 5a)(x-y)
9x(x^2y^2 - 4)
The second is the difference to two squares
(a^2 - b^2) (a+b)(a-b)
9x(xy+2)(xy-2)
Factor 6 out of the first two terms
6(x-y)
Factor -5a out of the third and fourth
-5a(x - y)
Since there is the common factor of (x-y)
(6 - 5a)(x-y)
參考: Longtime college math teacher
http://www.CharlesAshbacher.net
2008-10-11 4:09 pm
1)
9x^3y^2 - 36x
= 9(x^3y^2 - 4x)
= 9x(x^2y^2 - 4)
= 9x(x^2y^2 + 2xy - 2xy - 4)
= 9x[(x^2y^2 + 2xy) - (2xy + 4)]
= 9x[xy(xy + 2) - 2(xy + 2)]
= 9x(xy + 2)(xy - 2)
2)
6x - 6y - 5ax + 5ay
= (6x - 6y) - (5ax - 5ay)
= 6(x - y) - 5a(x - y)
= (x - y)(6 - 5a)
9x^3y^2 - 36x
= 9(x^3y^2 - 4x)
= 9x(x^2y^2 - 4)
= 9x(x^2y^2 + 2xy - 2xy - 4)
= 9x[(x^2y^2 + 2xy) - (2xy + 4)]
= 9x[xy(xy + 2) - 2(xy + 2)]
= 9x(xy + 2)(xy - 2)
2)
6x - 6y - 5ax + 5ay
= (6x - 6y) - (5ax - 5ay)
= 6(x - y) - 5a(x - y)
= (x - y)(6 - 5a)
2008-10-11 3:58 pm
9x(x^2 y^2 - 4)
9x(xy - 2) (xy + 2)
6x - 6y - 5ax + 5ay
= 6(x - y) - 5a (x - y)
= (6 - 5a) (x - y)
9x(xy - 2) (xy + 2)
6x - 6y - 5ax + 5ay
= 6(x - y) - 5a (x - y)
= (6 - 5a) (x - y)
2008-10-11 3:53 pm
9x (x^2y^2 - 4)
=9x(xy-2)(xy+2)
________________________________________________________
6(x-y) - 5a(x-y)
(6 -- 5a) ( x-y)
=9x(xy-2)(xy+2)
________________________________________________________
6(x-y) - 5a(x-y)
(6 -- 5a) ( x-y)
2008-10-11 3:52 pm
1. 9x(xy-2)(xy+2)
2. 6(x-y) - 5a(x-y) = (6-5a)(x-y)
2. 6(x-y) - 5a(x-y) = (6-5a)(x-y)
2008-10-11 3:52 pm
9x(x^2y^2 - 4)
9x(xy+2)(xy-2)
6(x-y) - 5a(x-y)
(6-5a)(x-y)
9x(xy+2)(xy-2)
6(x-y) - 5a(x-y)
(6-5a)(x-y)
2008-10-11 3:52 pm
9x (x²y - 4)
6(x-y) - 5a (x-y)
6(x-y) - 5a (x-y)
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