因式分解 36(2x-y)^2-25(u-2y)^2

解答

因式分解

36 (2 x - y)^{2} - 25 (u - 2 y)^{2}

(12 x - 16 y + 5 u) (12 x + 4 y - 5 u)

求解步骤

36 (2 x - y)^{2} - 25 (u - 2 y)^{2}

36 (2 x - y)^{2} = (6 (2 x - y))^{2}

25 (u - 2 y)^{2} = (5 (u - 2 y))^{2}

= (6 (2 x - y))^{2} - (5 (u - 2 y))^{2}

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

(6 (2 x - y))^{2} - (5 (u - 2 y))^{2} = (6 (2 x - y) + 5 (u - 2 y)) (6 (2 x - y) - 5 (u - 2 y))

= (6 (2 x - y) + 5 (u - 2 y)) (6 (2 x - y) - 5 (u - 2 y))

化简

(6 (2 x - y) + 5 (u - 2 y)) (6 (2 x - y) - 5 (u - 2 y)) : (12 x - 16 y + 5 u) (12 x + 4 y - 5 u)

= (12 x - 16 y + 5 u) (12 x + 4 y - 5 u)

f = 1 - \frac{2}{5} (3)

10 k - 1 < 8 k - 10

s im pl i f y (- 2 - 2 i) (- 4 - 3 i) (7 + 8 i)

s im pl i f y \frac{1}{3} - \frac{4}{3}

f a c t or 5 mn + 25 m + 3 n^{3} + 15 n^{2}