因式分解 9(x+2)^2-(x-1)^2

解答

因式分解

9 (x + 2)^{2} - (x - 1)^{2}

(4 x + 5) (2 x + 7)

求解步骤

9 (x + 2)^{2} - (x - 1)^{2}

化简

9 (x + 2)^{2} : (3 (x + 2))^{2}

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

使用平方差公式:

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

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

= (3 (x + 2) + (x - 1)) (3 (x + 2) - (x - 1))

化简

(3 (x + 2) + (x - 1)) (3 (x + 2) - (x - 1)) : (4 x + 5) (2 x + 7)

= (4 x + 5) (2 x + 7)

\frac{x}{x + 1} - \frac{2}{x + 2} \geq 1

1 5^{2} + x^{2} = 1 7^{2}

3 + 3 p > 9

\frac{x + 4}{x + 12} \leq 10

4 < \frac{p}{8}