展开 (2x^2+4y)^3

解答

展开

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

8 x^{6} + 48 x^{4} y + 96 x^{2} y^{2} + 64 y^{3}

求解步骤

(2 x^{2} + 4 y)^{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^{2} + 4 y)^{3} = (2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 4 y + 3 \cdot 2 x^{2} (4 y)^{2} + (4 y)^{3}

= (2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 4 y + 3 \cdot 2 x^{2} (4 y)^{2} + (4 y)^{3}

化简

(2 x^{2})^{3} + 3 (2 x^{2})^{2} \cdot 4 y + 3 \cdot 2 x^{2} (4 y)^{2} + (4 y)^{3} : 8 x^{6} + 48 x^{4} y + 96 x^{2} y^{2} + 64 y^{3}

= 8 x^{6} + 48 x^{4} y + 96 x^{2} y^{2} + 64 y^{3}

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

s im pl i f y lo g_{8} (2)

s im pl i f y \frac{13}{39}

s im pl i f y \frac{\frac{8 r + 8 s}{r ^{2}}}{\frac{r ^{2} - s ^{2}}{8 r}}

s im pl i f y (x y^{2} - 3 x^{2} - y^{2} + x^{2} y) + (x^{2} y + 5 x^{2}) + (3 x y^{2} - y^{2} - 5 x^{2})