展开 (2x+3z)^3

解答

展开

(2 x + 3 z)^{3}

8 x^{3} + 36 x^{2} z + 54 x z^{2} + 27 z^{3}

求解步骤

(2 x + 3 z)^{3}

使用完全立方公式:

(a + b)^{3} = a^{3} + 3 a^{2} b + 3 a b^{2} + b^{3}

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

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

化简

(2 x)^{3} + 3 (2 x)^{2} \cdot 3 z + 3 \cdot 2 x (3 z)^{2} + (3 z)^{3} : 8 x^{3} + 36 x^{2} z + 54 x z^{2} + 27 z^{3}

= 8 x^{3} + 36 x^{2} z + 54 x z^{2} + 27 z^{3}

f a c t or 81 y^{4} - 625

f a c t or 125 x^{3} + 64 y^{3}

s im pl i f y a (- a)^{3}

s im pl i f y (v) \cdot (2 x^{2} + 3)^{\frac{5}{3}} \cdot (x + 5)^{\frac{- 1}{2}}

s im pl i f y 1 - \frac{\frac{3}{( x + 6 )}}{x} + \frac{9}{( x + 6 )}