展開する (((Ax)-1)^2)/(((Bx)-1)^2((Cx)-1)^2)

解

展開する

\frac{( ( A \cdot x ) - 1 ) ^{2}}{( ( B \cdot x ) - 1 ) ^{2} \cdot ( ( C \cdot x ) - 1 ) ^{2}}

\frac{A ^{2} x ^{2} - 2 A x + 1}{B ^{2} C ^{2} x ^{4} - 2 B ^{2} C x ^{3} + B ^{2} x ^{2} - 2 B C ^{2} x ^{3} + 4 BC x ^{2} - 2 B x + C ^{2} x ^{2} - 2 C x + 1}

解答ステップ

\frac{( ( A x ) - 1 ) ^{2}}{( ( B x ) - 1 ) ^{2} ( ( C x ) - 1 ) ^{2}}

括弧を削除する:

(a) = a

= \frac{( A x - 1 ) ^{2}}{( B x - 1 ) ^{2} ( C x - 1 ) ^{2}}

(B x - 1)^{2} = B^{2} x^{2} - 2 B x + 1

= \frac{( A x - 1 ) ^{2}}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C x - 1 ) ^{2}}

(C x - 1)^{2} = C^{2} x^{2} - 2 C x + 1

= \frac{( A x - 1 ) ^{2}}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C ^{2} x ^{2} - 2 C x + 1 )}

(A x - 1)^{2} = A^{2} x^{2} - 2 A x + 1

= \frac{A ^{2} x ^{2} - 2 A x + 1}{( B ^{2} x ^{2} - 2 B x + 1 ) ( C ^{2} x ^{2} - 2 C x + 1 )}

拡張

(B^{2} x^{2} - 2 B x + 1) (C^{2} x^{2} - 2 C x + 1) : B^{2} C^{2} x^{4} - 2 B^{2} C x^{3} + B^{2} x^{2} - 2 B C^{2} x^{3} + 4 BC x^{2} - 2 B x + C^{2} x^{2} - 2 C x + 1

= \frac{A ^{2} x ^{2} - 2 A x + 1}{B ^{2} C ^{2} x ^{4} - 2 B ^{2} C x ^{3} + B ^{2} x ^{2} - 2 B C ^{2} x ^{3} + 4 BC x ^{2} - 2 B x + C ^{2} x ^{2} - 2 C x + 1}