因式分解 36x^2-84xy+49y^2

解答

因式分解

36 x^{2} - 84 x y + 49 y^{2}

(6 x - 7 y)^{2}

求解步骤

36 x^{2} - 84 x y + 49 y^{2}

改写为形式

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

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

49 y^{2} = (7 y)^{2}

- 84 x y = - 2 \cdot 6 x \cdot 7 y

= (6 x)^{2} - 2 \cdot 6 x \cdot 7 y + (7 y)^{2}

使用完全平方公式:

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

(6 x)^{2} - 2 \cdot 6 x \cdot 7 y + (7 y)^{2} = (6 x - 7 y)^{2}

= (6 x - 7 y)^{2}

3 m - 5 + 6 m - 3 + m - 7 = 2 m + 1

r^{2} + 6 r + 9 = 0

x^{2} - 4 = 10

s im pl i f y \frac{a}{b} - \frac{b}{a}

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