展开 (5e^3+4t^2)^2

解答

展开

(5 e^{3} + 4 t^{2})^{2}

16 t^{4} + 40 e^{3} t^{2} + 25 e^{6}

求解步骤

(5 e^{3} + 4 t^{2})^{2}

使用完全平方公式:

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

a = 5 e^{3}, b = 4 t^{2}

= (5 e^{3})^{2} + 2 \cdot 5 e^{3} \cdot 4 t^{2} + (4 t^{2})^{2}

化简

(5 e^{3})^{2} + 2 \cdot 5 e^{3} \cdot 4 t^{2} + (4 t^{2})^{2} : 25 e^{6} + 40 e^{3} t^{2} + 16 t^{4}

= 25 e^{6} + 40 e^{3} t^{2} + 16 t^{4}

改写为标准形式

= 16 t^{4} + 40 e^{3} t^{2} + 25 e^{6}

e x p an d [(2 x - 3) (2 x + 3)]^{2}

e x p an d (3 x^{2} + 6 x + 1)^{5}

e x p an d 5 x^{3} y (6 x y^{5})

e x p an d \frac{( 3 x - y ) ^{2}}{81}

e x p an d \frac{x ^{3}}{2 ( x ^{2} - 4 )}