展开 ((x^2)+1)^3

解答

展开

((x^{2}) + 1)^{3}

x^{6} + 3 x^{4} + 3 x^{2} + 1

求解步骤

((x^{2}) + 1)^{3}

化简

(x^{2}) + 1 : x^{2} + 1

= (x^{2} + 1)^{3}

使用完全立方公式:

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

(x^{2} + 1)^{3} = (x^{2})^{3} + 3 (x^{2})^{2} \cdot 1 + 3 x^{2} \cdot 1^{2} + 1^{3}

= (x^{2})^{3} + 3 (x^{2})^{2} \cdot 1 + 3 x^{2} \cdot 1^{2} + 1^{3}

化简

(x^{2})^{3} + 3 (x^{2})^{2} \cdot 1 + 3 x^{2} \cdot 1^{2} + 1^{3} : x^{6} + 3 x^{4} + 3 x^{2} + 1

= x^{6} + 3 x^{4} + 3 x^{2} + 1

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

f (x) = 3 + 4 x^{5}

s im pl i f y (a^{2} + 1)^{2} + (a^{2} + 5)^{2} - 4 \cdot (a^{2} + 3)^{2}

s im pl i f y (14.5 - 5.3) \cdot x^{2.5} + (3.5) 2

s im pl i f y \frac{( x ^{3} - 49 x )}{( x ^{4} - 7 x ^{3} )}