因式分解 9x^2-66x+121

解答

因式分解

9 x^{2} - 66 x + 121

(3 x - 11)^{2}

求解步骤

9 x^{2} - 66 x + 121

改写为形式

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

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

121 = 1 1^{2}

- 66 x = - 2 \cdot 3 x \cdot 11

= (3 x)^{2} - 2 \cdot 3 x \cdot 11 + 1 1^{2}

使用完全平方公式:

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

(3 x)^{2} - 2 \cdot 3 x \cdot 11 + 1 1^{2} = (3 x - 11)^{2}

= (3 x - 11)^{2}

9 x (x + 6) - (3 x + 1)^{2} = 1

f a c t or 3 k^{4} - 48 k^{2}

f a c t or 125 x^{2} - 80

x^{2} = 400

f a c t or 125 + a^{3}