因式分解(用恆等式)

hong kong

2008-11-05 6:37 am

1) 2(7x+y)二次方-50(x-y)二次方
2)4x二次方-9y二次方-2x-3y
3)9x二次方-y二次方+(3x+y)二次方
4)9x-y二次方+(3x+y)二次方
5)3b四次方-768

回答 (1)

用戶10012

2008-11-05 6:58 am

✔ 最佳答案

1. 2(7+y)^2 - 50(x-y)^2
= 2[(7+y)^2 - 25(x-y)^]
= 2{(7+y)^2 - [5(x-y)^2]}
= 2[7+y -5(x-y)][7+y + 5(x-y)]
= 2(7 - 5x + 6y)(7 + 5x - 4y).
2.
4x^2 - 9y^2 - 2x - 3y
= (2x)^2 - (3y)^2 - (2x + 3y)
= (2x + 3y)(2x -3y) - (2x +3y)
= (2x +3y)(2x - 3y - 1).
3.
= (3x)^2 - y^2 + (3x + y)^2
= (3x +y)(3x -y) + (3x +y)^2
= (3x +y)(3x - y + 3x + y)
= 6x(3x+y).
4.
= 9x - y^2 + (3x +y)^2
= 9x + (3x + y + y)(3x + y - y)
= 9x + (3x + 2y)(3x)
= 3x(3 + 3x + 2y).
5.
3b^4 - 768
= 3(b^4 - 256)
= 3(b^4 - 4^4)
= 3(b^2 + 16)(b^2 - 4^2)
= 3(b^2 + 16)(b-4)(b+4).

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