展開する (1+7/2 x)(2-9x)^4

解

展開する

(1 + \frac{7}{2} x) (2 - 9 x)^{4}

- 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16

解答ステップ

(1 + \frac{7}{2} x) (2 - 9 x)^{4}

= (2 - 9 x)^{4} (1 + \frac{7}{2} x)

分配法則を適用する:

a (b + c) = ab + a c

(2 - 9 x)^{4} (1 + \frac{7}{2} x) = (2 - 9 x)^{4} \cdot 1 + (2 - 9 x)^{4} \frac{7}{2} x

= (2 - 9 x)^{4} \cdot 1 + (2 - 9 x)^{4} \frac{7}{2} x

規則を適用する:

a \cdot 1 = a

(2 - 9 x)^{4} \cdot 1 = (2 - 9 x)^{4}

= (2 - 9 x)^{4} + (2 - 9 x)^{4} \frac{7}{2} x

= (2 - 9 x)^{4} + \frac{7}{2} x (2 - 9 x)^{4}

拡張

(2 - 9 x)^{4} : 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4}

= 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + \frac{7}{2} x (2 - 9 x)^{4}

拡張

\frac{7}{2} x (2 - 9 x)^{4} : 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2}

= 16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2}

簡素化

16 - 288 x + 1944 x^{2} - 5832 x^{3} + 6561 x^{4} + 56 x - 1008 x^{2} + 6804 x^{3} - 20412 x^{4} + \frac{45927 x ^{5}}{2} : - 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16

= - 13851 x^{4} + 972 x^{3} + 936 x^{2} - 232 x + \frac{45927 x ^{5}}{2} + 16