展开 (3x+4sqrt(x+1)+1)^2

解答

展开

(3 x + 4 x + 1 + 1)^{2}

9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

求解步骤

(3 x + 4 x + 1 + 1)^{2}

使用指数法则:

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

(3 x + 4 x + 1 + 1)^{2} = (3 x + 4 x + 1 + 1) (3 x + 4 x + 1 + 1)

= (3 x + 4 x + 1 + 1) (3 x + 4 x + 1 + 1)

打开括号

= 3 x \cdot 3 x + 3 x \cdot 4 x + 1 + 3 x \cdot 1 + 4 x + 1 \cdot 3 x + 4 x + 1 \cdot 4 x + 1 + 4 x + 1 \cdot 1 + 1 \cdot 3 x + 1 \cdot 4 x + 1 + 1 \cdot 1

化简

3 x \cdot 3 x + 3 x \cdot 4 x + 1 + 3 x \cdot 1 + 4 x + 1 \cdot 3 x + 4 x + 1 \cdot 4 x + 1 + 4 x + 1 \cdot 1 + 1 \cdot 3 x + 1 \cdot 4 x + 1 + 1 \cdot 1 : 9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

= 9 x^{2} + 22 x + 24 x x + 1 + 8 x + 1 + 17

e x p an d (\frac{12}{25}) \cdot (\frac{- 4}{5})

e x p an d \frac{( x - 5 ) ( x ^{2} + 5 x + 4 )}{x ^{2} - 2 x - 8}

e x p an d 2 p 1 + x^{2} + p (50 - x)

e x p an d 9 e^{2} x (20 x^{2} + 5)

s im pl i f y (F \cdot x - \frac{F \cdot L \cdot x}{a}) \cdot (x - \frac{L \cdot x}{a})