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受欢迎的代数 >

展开 (1+w^2)^4

解答

展开

(1 + w^{2})^{4}

解答

1 + 4 w^{2} + 6 w^{4} + 4 w^{6} + w^{8}

求解步骤

(1 + w^{2})^{4}

使用二项式定理:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 1, b = w^{2}

= i = 0 \sum 4 (i 4) \cdot 1^{(4 - i)} (w^{2})^{i}

展开求和

= \frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (w^{2})^{0} + \frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (w^{2})^{1} + \frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (w^{2})^{2} + \frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (w^{2})^{3} + \frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (w^{2})^{4}

化简

\frac{4 !}{0 ! ( 4 - 0 ) !} \cdot 1^{4} (w^{2})^{0} : 1

化简

\frac{4 !}{1 ! ( 4 - 1 ) !} \cdot 1^{3} (w^{2})^{1} : 4 w^{2}

化简

\frac{4 !}{2 ! ( 4 - 2 ) !} \cdot 1^{2} (w^{2})^{2} : 6 w^{4}

化简

\frac{4 !}{3 ! ( 4 - 3 ) !} \cdot 1^{1} (w^{2})^{3} : 4 w^{6}

化简

\frac{4 !}{4 ! ( 4 - 4 ) !} \cdot 1^{0} (w^{2})^{4} : w^{8}

= 1 + 4 w^{2} + 6 w^{4} + 4 w^{6} + w^{8}

流行的例子

因式分解 x^4-14x^2y^2-51y^4

f a c t or x^{4} - 14 x^{2} y^{2} - 51 y^{4}

化简 x^{109}*2*10x^5x^{1045}*10-2x^{10}

s im pl i f y x^{109} \cdot 2 \cdot 10 x^{5} x^{1045} \cdot 10 - 2 x^{10}

因式分解 a^2+5a-36

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

因式分解 v^2*w^2-64

f a c t or v^{2} \cdot w^{2} - 64

化简-3+3/x-1/3

s im pl i f y - 3 + \frac{3}{x} - \frac{1}{3}