因式分解 4x^2-9y^2

解答

因式分解

4 x^{2} - 9 y^{2}

(2 x + 3 y) (2 x - 3 y)

求解步骤

4 x^{2} - 9 y^{2}

4 x^{2} = (2 x)^{2}

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

= (2 x)^{2} - (3 y)^{2}

使用平方差公式:

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

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

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

\frac{x + 5}{3} + \frac{x + 1}{2} = 8

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

2 x^{2} + 4 x + 12 = 0

f a c t or 3 p^{2} - 75

- 1 \leq 4 x + 3 < 11