Question

[Nguyễn Hải Đăng]

Khai triển hằng đẳng thức:
a) (3x+1)³
b) (x/3-1)
c) (2x-1/x)³
d)(-y²+3x)³
e)(y-xy/3)³
 

Answer 1

[Huỳnh Quang Sang]

Áp dụng công thức : (A + B)³ = A³ + 3A²B + 3AB² + B³

(A - B)³ = A³ - 3A²B + 3AB² -B³

a) (3x + 1)³ = (3x)³ + 3.(3x)².1 + 3.3x.1 + 1³ = 27x³ + 27x² + 9x + 1

b) \(\left(\frac{x}{3}-1\right)^3=\left(\frac{x}{3}\right)^3-3\cdot\left(\frac{x}{3}\right)^2\cdot1+3\cdot\left(\frac{x}{3}\right)\cdot1^2-1^3\)

\(=\frac{x^3}{27}-3\cdot\frac{x^2}{9}\cdot1+3\cdot\frac{x}{3}\cdot1-1\)

= \(\frac{x^3}{27}-\frac{x^2}{3}+x-1\)

c) \(\left(2x-\frac{1}{x}\right)^3=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot\frac{1}{x}+3\cdot2x\cdot\left(\frac{1}{x}\right)^2-\left(\frac{1}{x}\right)^3\)

\(=8x^3-3\cdot4x^2\cdot\frac{1}{x}+6x\cdot\frac{1}{x^2}-\frac{1}{x^3}\)

\(=8x^3-12x+\frac{6}{x}-\frac{1}{x^3}\)

d) \(\left(-y^2+3x\right)^3=\left(3x-y^2\right)^3=\left(3x\right)^3-3\cdot\left(3x\right)^2\cdot y^2+3\cdot3x\cdot y^4-y^6\)

= 27x³ - 27x²y² + 9xy⁴ - y⁶

= -y⁶ + 9xy⁴ - 27x²y² + 27x³

Tương tự câu cuối :>