展开 x(1-x-y)^2

解答

展开

x (1 - x - y)^{2}

2 x^{2} y - 2 x^{2} + x^{3} - 2 x y + x y^{2} + x

求解步骤

x (1 - x - y)^{2}

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

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

打开括号

= x \cdot 2 x y + x (- 2 x) + x x^{2} + x (- 2 y) + x y^{2} + x \cdot 1

使用加减运算法则

+ (- a) = - a

= 2 xx y - 2 xx + x^{2} x - 2 x y + x y^{2} + 1 \cdot x

化简

2 xx y - 2 xx + x^{2} x - 2 x y + x y^{2} + 1 \cdot x : 2 x^{2} y - 2 x^{2} + x^{3} - 2 x y + x y^{2} + x

= 2 x^{2} y - 2 x^{2} + x^{3} - 2 x y + x y^{2} + x

e x p an d (12 y + 2 t - 5) d t + (6 y + 12 t - 1) d y

e x p an d (3 (x - 2 y) + 2 (x + 3) = 4,) (4 (x + y) - 3 (x + 2 y) = - 2)

e x p an d (4 x + 5) (x ln (x) - x)

e x p an d e^{t - 2} U (t - 2)

e x p an d \frac{x ^{5} + 1}{( x ^{2} - x ) ( x ^{4} + 2 x ^{2} + 1 )}