因式分解 9w^2-48wv+64v^2

解答

因式分解

9 w^{2} - 48 w v + 64 v^{2}

(3 w - 8 v)^{2}

求解步骤

9 w^{2} - 48 w v + 64 v^{2}

改写为形式

a^{2} + 2 ab + b^{2} :

9 w^{2} = (3 w)^{2}

64 v^{2} = (8 v)^{2}

- 48 w v = - 2 \cdot 3 w \cdot 8 v

= (3 w)^{2} - 2 \cdot 3 w \cdot 8 v + (8 v)^{2}

使用完全平方公式:

a^{2} - 2 ab + b^{2} = (a - b)^{2}

(3 w)^{2} - 2 \cdot 3 w \cdot 8 v + (8 v)^{2} = (3 w - 8 v)^{2}

= (3 w - 8 v)^{2}

s im pl i f y \frac{2}{3} + \frac{1}{2} - \frac{1}{3}

2 (- 2)^{3} + 3 (- 2)^{2} - 12 (- 2) + 6

\frac{1}{2} - \frac{m}{8} < \frac{7}{8}

f a c t or 8 a^{2} - 14 a - 15

(x - 4)^{2} (16 - 2 x) > 0