因式分解 49x^2-84xy+36y^2

解答

因式分解

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

(7 x - 6 y)^{2}

求解步骤

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

改写为形式

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

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

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

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

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

使用完全平方公式:

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

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

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

x (x + 3)^{2} (x - 1) \leq 0

x^{2} - 7 x - 6 = 0

s im pl i f y \frac{10 x ^{5} y ^{3}}{15 x ^{8} y ^{4}}

f a c t or 4 n^{2} + 4 n + 1

x^{2} - 6 x = - 2