확장 (b/a (x-z)+y+c)^3

해법

확장

(\frac{b}{a} (x - z) + y + c)^{3}

\frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}

솔루션 단계

(\frac{b}{a} (x - z) + y + c)^{3}

(\frac{b}{a} (x - z) + y + c)^{3}

간소화하다 :

(\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

= (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

(\frac{b}{a} (x - z) + y + c) (\frac{b}{a} (x - z) + y + c)

확장 :

\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} + y^{2} + 2 cy + c^{2}

= (\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} + y^{2} + 2 cy + c^{2}) (\frac{b}{a} (x - z) + y + c)

괄호 배포

= \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} \cdot \frac{b}{a} (x - z) + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} y + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} c + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} \cdot \frac{b}{a} (x - z) + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} y + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} c + y^{2} \frac{b}{a} (x - z) + y^{2} y + y^{2} c + 2 cy \frac{b}{a} (x - z) + 2 cyy + 2 cyc + c^{2} \frac{b}{a} (x - z) + c^{2} y + c^{2} c

\frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} \cdot \frac{b}{a} (x - z) + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} y + \frac{b ^{2} ( x - z ) ( x - z )}{a ^{2}} c + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} \cdot \frac{b}{a} (x - z) + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} y + \frac{2 b x y - 2 b zy + 2 b c x - 2 b cz}{a} c + y^{2} \frac{b}{a} (x - z) + y^{2} y + y^{2} c + 2 cy \frac{b}{a} (x - z) + 2 cyy + 2 cyc + c^{2} \frac{b}{a} (x - z) + c^{2} y + c^{2} c

간소화하다 :

\frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}

= \frac{b ^{3} ( x - z ) ( x - z ) ( x - z )}{a ^{3}} + \frac{3 b ^{2} x ^{2} y + 3 b ^{2} z ^{2} y + 3 b ^{2} x ^{2} c + 3 b ^{2} z ^{2} c - 6 x b ^{2} zy - 2 x b ^{2} cz - 2 c x b ^{2} z - 2 b ^{2} c x z}{a ^{2}} + \frac{3 b x y ^{2} - 3 b z y ^{2} + 3 b x c ^{2} - 3 b z c ^{2} + 6 b c x y - 6 b czy}{a} + y^{3} + 3 c y^{2} + 3 y c^{2} + c^{3}