展开 (x^2-x(d+c)+dc)(x^2-x(e+b)+eb)

解答

展开

(x^{2} - x (d + c) + d c) (x^{2} - x (e + b) + e b)

x^{4} - e x^{3} - b x^{3} + e b x^{2} - d x^{3} - c x^{3} + e d x^{2} + d b x^{2} + ec x^{2} + c b x^{2} - e d b x - ec b x + d c x^{2} - e d c x - d c b x + e d c b

求解步骤

(x^{2} - x (d + c) + d c) (x^{2} - x (e + b) + e b)

打开括号

= x^{2} x^{2} + x^{2} (- x (e + b)) + x^{2} e b + (- x (d + c)) x^{2} + (- x (d + c)) (- x (e + b)) + (- x (d + c)) e b + d c x^{2} + d c (- x (e + b)) + d ce b

使用加减运算法则

+ (- a) = - a, (- a) (- b) = ab

= x^{2} x^{2} - x^{2} x (e + b) + e b x^{2} - x^{2} x (d + c) + xx (d + c) (e + b) - e b x (d + c) + d c x^{2} - d c x (e + b) + e d c b

化简

x^{2} x^{2} - x^{2} x (e + b) + e b x^{2} - x^{2} x (d + c) + xx (d + c) (e + b) - e b x (d + c) + d c x^{2} - d c x (e + b) + e d c b : x^{4} - e x^{3} - b x^{3} + e b x^{2} - d x^{3} - c x^{3} + e d x^{2} + d b x^{2} + ec x^{2} + c b x^{2} - e d b x - ec b x + d c x^{2} - e d c x - d c b x + e d c b

= x^{4} - e x^{3} - b x^{3} + e b x^{2} - d x^{3} - c x^{3} + e d x^{2} + d b x^{2} + ec x^{2} + c b x^{2} - e d b x - ec b x + d c x^{2} - e d c x - d c b x + e d c b

e x p an d \frac{( 3 x + 2 ) ( 3 x - 2 )}{9 x ^{2} + 4}

e x p an d 9 (\frac{x}{9} + \frac{y}{1} = 1)

e x p an d \frac{3 ( x + 4 )}{2}

s im pl i f y 4 (n + 2 i)^{2}

e x p an d \frac{2 ( 2 x + 3 )}{3 x + 2}