展开 (5x^2+7y^3)^3

解答

展开

(5 x^{2} + 7 y^{3})^{3}

125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

求解步骤

(5 x^{2} + 7 y^{3})^{3}

使用完全立方公式:

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

(5 x^{2} + 7 y^{3})^{3} = (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

= (5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3}

化简

(5 x^{2})^{3} + 3 (5 x^{2})^{2} \cdot 7 y^{3} + 3 \cdot 5 x^{2} (7 y^{3})^{2} + (7 y^{3})^{3} : 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

= 125 x^{6} + 525 x^{4} y^{3} + 735 x^{2} y^{6} + 343 y^{9}

s im pl i f y (\frac{x ^{2}}{y ^{- 2}})^{- 2} (\frac{3 y ^{- 3}}{x ^{2}})^{3}

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

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

s im pl i f y a (a + b)^{3} - 3 a^{2} b (a + b)

f a c t or 9 x^{2} + 6 x + 1 - 25 y^{2}