展开 (6a+3b+5c)^2

解答

展开

(6 a + 3 b + 5 c)^{2}

36 a^{2} + 36 ab + 60 a c + 9 b^{2} + 30 b c + 25 c^{2}

求解步骤

(6 a + 3 b + 5 c)^{2}

使用指数法则:

a^{b + c} = a^{b} \cdot a^{c}

(6 a + 3 b + 5 c)^{2} = (6 a + 3 b + 5 c) (6 a + 3 b + 5 c)

= (6 a + 3 b + 5 c) (6 a + 3 b + 5 c)

打开括号

= 6 a \cdot 6 a + 6 a \cdot 3 b + 6 a \cdot 5 c + 3 b \cdot 6 a + 3 b \cdot 3 b + 3 b \cdot 5 c + 5 c \cdot 6 a + 5 c \cdot 3 b + 5 c \cdot 5 c

化简

6 a \cdot 6 a + 6 a \cdot 3 b + 6 a \cdot 5 c + 3 b \cdot 6 a + 3 b \cdot 3 b + 3 b \cdot 5 c + 5 c \cdot 6 a + 5 c \cdot 3 b + 5 c \cdot 5 c : 36 a^{2} + 36 ab + 60 a c + 9 b^{2} + 30 b c + 25 c^{2}

= 36 a^{2} + 36 ab + 60 a c + 9 b^{2} + 30 b c + 25 c^{2}

s im pl i f y \frac{( n + 10 ) !}{( n + 9 ) !}

f a c t or 81 x^{4} - 9 x^{2} + 6 x - 1

f a c t or x^{4} + 12 x^{2} y^{2} + 64 y^{4}

s im pl i f y \frac{- 8}{25 x - 50}

e x p an d (1 + 2 x + y)^{2}