因式分解 25x^2+30xy+9y^2

解答

因式分解

25 x^{2} + 30 x y + 9 y^{2}

(5 x + 3 y)^{2}

求解步骤

25 x^{2} + 30 x y + 9 y^{2}

改写为形式

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

25 x^{2} = (5 x)^{2}

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

30 x y = 2 \cdot 5 x \cdot 3 y

= (5 x)^{2} + 2 \cdot 5 x \cdot 3 y + (3 y)^{2}

使用完全平方公式:

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

(5 x)^{2} + 2 \cdot 5 x \cdot 3 y + (3 y)^{2} = (5 x + 3 y)^{2}

= (5 x + 3 y)^{2}

f a c t or 2 b^{2} + 9 b + 9

0.6 n \geq 12 - 0.4 n

3 (4 x - 1) - 2 (5 x - 3) = 11 - 2 x

4 x - 13 = 2 x + 9

x^{2} + x - 72 \geq 0