兩條爆難既數(對我泥讲)

這兩條因式分解主要應用以下公式：a² - b² = (a + b)(a – b)

1)
25(x + 1)² - 16(x - 1)²
= [5(x + 1)]² - [4(x -1)]²
= (5x + 5)² - (4x - 4)²
= [(5x + 5) + (4x - 4)] [(5x + 5) - (4x - 4)]
= (5x + 5 + 4x - 4)(5x + 5 - 4x + 4)
= (9x + 1)(x + 9)

2)
m(x + y)² - 4m(x - y)²= m[(x + y)² - 4(x - y)²]
= m{(x + y)² - [2(x - y)]²}
= m[(x + y)² - (2x - 2y)]
= m[(x + y) + (2x - 2y)] [(x + y) - (2x - 2y)]
= m(x + y + 2x - 2y)(x + y - 2x + 2y)
= m(3x - y)(3y - x)

2010-09-30 13:34:47 補充：
另一方法：

1)
25(x + 1)² - 16(x - 1)²
= 25(x² + 2x + 1) – 16(x² - 2x + 1)
= 25x² + 50x + 25 – 16x² + 32x - 16
= 9x² + 82x + 9
= (9x + 1)(x + 9)

2010-09-30 13:34:56 補充：
2)
m(x + y)² - 4m(x - y)²
= m(x² + 2xy + y²) - 4m(x² - 2xy + y²)
= m(x² + 2xy + y²) - m(4x² - 8xy + 4y²)
= m[(x² + 2xy + y²) - (4x² - 8xy + 4y²)]
= m[x² + 2xy + y² - 4x² + 8xy - 4y²]
= m(-3x² + 10xy - 3y²)
= m(3x - y)(-x + 3y)
= m(3x - y)(3y - x)
(or: -m(3x - y)(x - 3y))

請問題目是否要求因式分解? 謝謝!

1. 25(x+1)^2 -16(x-1)^2
=25(x^2 +2x +1) - 16(x^2 -2x +1)
=25x^2 +50x +25 - (16x^2 -32x +16)
=9x^2+82x+9
=(9x+1)(x+9)

2.m(x+y)^2 -4m(x-y)^2
=m(x^2 +2yx +y^2) -4m(x^2 -2yx +y^2)
=mx^2 +2myx +my^2 -4mx^2 +8myx -4my^2
=-3mx^2 +10myx -3my^2
=(3mx-my)(x-3my)