展開する ((k)(2p+1)^2)/(p(0.5p+1)^2(p^2+p+1))

解

展開する

\frac{( k ) ( 2 p + 1 ) ^{2}}{p ( 0.5 p + 1 ) ^{2} ( p ^{2} + p + 1 )}

\frac{4 k p ^{2} + 4 k p + k}{0.25 p ^{5} + 1.25 p ^{4} + 2.25 p ^{3} + 2 p ^{2} + p}

解答ステップ

\frac{( k ) ( 2 p + 1 ) ^{2}}{p ( 0.5 p + 1 ) ^{2} ( p ^{2} + p + 1 )}

括弧を削除する:

(a) = a

= \frac{k ( 2 p + 1 ) ^{2}}{p ( 0.5 p + 1 ) ^{2} ( p ^{2} + p + 1 )}

(0.5 p + 1)^{2} = 0.25 p^{2} + p + 1

= \frac{k ( 2 p + 1 ) ^{2}}{p ( 0.25 p ^{2} + p + 1 ) ( p ^{2} + p + 1 )}

(2 p + 1)^{2} = 4 p^{2} + 4 p + 1

= \frac{k ( 4 p ^{2} + 4 p + 1 )}{p ( 0.25 p ^{2} + p + 1 ) ( p ^{2} + p + 1 )}

拡張

p (0.25 p^{2} + p + 1) (p^{2} + p + 1) : 0.25 p^{5} + 1.25 p^{4} + 2.25 p^{3} + 2 p^{2} + p

= \frac{k ( 4 p ^{2} + 4 p + 1 )}{0.25 p ^{5} + 1.25 p ^{4} + 2.25 p ^{3} + 2 p ^{2} + p}

拡張

k (4 p^{2} + 4 p + 1) : 4 k p^{2} + 4 k p + k

= \frac{4 k p ^{2} + 4 k p + k}{0.25 p ^{5} + 1.25 p ^{4} + 2.25 p ^{3} + 2 p ^{2} + p}