展开 (1+2x+3x^2)^2

解答

展开

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

9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

求解步骤

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

使用指数法则:

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

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

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

打开括号

= 1 \cdot 1 + 1 \cdot 2 x + 1 \cdot 3 x^{2} + 2 x \cdot 1 + 2 x \cdot 2 x + 2 x \cdot 3 x^{2} + 3 x^{2} \cdot 1 + 3 x^{2} \cdot 2 x + 3 x^{2} \cdot 3 x^{2}

化简

1 \cdot 1 + 1 \cdot 2 x + 1 \cdot 3 x^{2} + 2 x \cdot 1 + 2 x \cdot 2 x + 2 x \cdot 3 x^{2} + 3 x^{2} \cdot 1 + 3 x^{2} \cdot 2 x + 3 x^{2} \cdot 3 x^{2} : 9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

= 9 x^{4} + 12 x^{3} + 10 x^{2} + 4 x + 1

s im pl i f y \frac{e ^{- x} - e ^{- x} x}{e ^{x}}

s im pl i f y 7 (16)

e x p an d 5 (x + 1) (x + 2)

f a c t or 5 x^{2} + 11 x - 36

s im pl i f y 12 e^{0.8}