(x - 1/2 )(x + 1/2 )(4x - 1)

= ( x 2  + 1/2 x - 1/2 x - 1/4 )(4x - 1)

= ( x 2  - 1/4 )(4x - 1)

= 4 x 3  –  x 2  – x + 1/4

Bài 3:

3: \(6x\left(x-y\right)-9y^2+9xy\)

\(=6x\left(x-y\right)+9xy-9y^2\)

\(=6x\left(x-y\right)+9y\left(x-y\right)\)

\(=\left(x-y\right)\left(6x+9y\right)\)

\(=3\left(2x+3y\right)\left(x-y\right)\)

Bài 4:

Bạn cần viết lại đề bằng công thức toán (biểu tượng $\sum$ góc trái khung soạn thảo). Viết như thế này nhìn khó đọc quá.

a: \(=2x+x^3-5x^4\)

b: \(=\dfrac{8x^2+4x-7x-3}{\left(2x-1\right)\left(2x+1\right)}=\dfrac{8x^2-3x-3}{\left(2x-1\right)\left(2x+1\right)}\)

Trả lời:

a, ( x + 1 )² + ( x - 2 ) ( x + 3 ) - 4x 

= x² + 2x + 1 + x² + 3x - 2x - 6 - 4x

= 2x² - x - 5

b, ( x - 2 )² + ( x + 1 )² + 2 ( x - 2 ) ( - 1 - x ) 

= x² - 4x - 4 + x² + 2x + 1 + ( 2x - 4 ) ( - 1 - x )

= 2x² - 2x - 3 - 2x - 2x² + 4x + 4x

= 4x - 3

a) \(\left(x+1\right)^2+\left(x-2\right)\left(x+3\right)-4x\)

\(=\left(x^2+2x+1\right)+\left(x^2+x-6\right)-4x\)

\(=x^2+2x+1+x^2+x-6-4x\)

\(=2x^2-x-5\)

b) \(\left(x-2\right)^2+\left(x+1\right)^2+2\left(x-2\right)\left(-1-x\right)\)

\(=\left(x^2-4x+4\right)+\left(x^2+2x+1\right)+\left(2x-4\right)\left(-1-x\right)\)

\(=x^2-4x+4+x^2+2x+1+\left(-2x-2x^2+4+4x\right)\)

\(=x^2-4x+4+x^2+2x+1-2x-2x^2+4+4x\)

\(=9\)

Ta có: \(\left(\dfrac{x+2}{3x}+\dfrac{2}{x+1}-3\right):\dfrac{2-4x}{x+1}\cdot\dfrac{3x}{x^2-3x-1}\)

\(=\left(\dfrac{\left(x+2\right)\left(x+1\right)}{3x\left(x+1\right)}+\dfrac{6x}{3x\left(x+1\right)}-\dfrac{9x\left(x+1\right)}{3x\left(x+1\right)}\right):\dfrac{2-4x}{x+1}\cdot\dfrac{3x}{x^2-3x-1}\)

\(=\dfrac{x^2+3x+2+6x-9x^2-9x}{3x\left(x+1\right)}\cdot\dfrac{x+1}{2-4x}\cdot\dfrac{3x}{x^2-3x-1}\)

\(=\dfrac{-8x^2+2}{3x\left(x+1\right)}\cdot\dfrac{x+1}{2-4x}\cdot\dfrac{3x}{x^2-3x-1}\)

\(=\dfrac{-2\left(4x^2-1\right)}{3x\cdot2\cdot\left(1-2x\right)}\cdot\dfrac{3x}{x^2-3x-1}\)

\(=\dfrac{2\left(1-2x\right)\left(2x+3\right)}{6x\left(1-2x\right)}\cdot\dfrac{3x}{x^2-3x-1}\)

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

Ta có \(\left(\frac{1}{x^2+4x+4}-\frac{1}{x^2-4x+4}\right):\left(\frac{1}{x+2}+\frac{1}{x-2}\right)\)

\(=\frac{\left(x-2\right)^2-\left(x+2\right)^2}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{x-2+x+2}{\left(x-2\right)\left(x+2\right)}\)

\(=\frac{\left(x-2+x+2\right)\left(x-2-x-2\right)}{\left(x-2\right)^2\left(x+2\right)^2}:\frac{2x}{\left(x+2\right)\left(x-2\right)}\)

\(\frac{-4.2x}{\left(x+2\right)^2\left(x-2\right)^2}.\frac{\left(x+2\right)\left(x-2\right)}{2x}=\frac{-4}{\left(x+2\right)\left(x-2\right)}\)

=3x(x^2-2)(3x^2+x-2)

=(3x^3-6x)(3x^2+x-2)

=9x^5+3x^4-6x^3-18x^3-6x^2+12x

=9x^5+3x^4-12x^3-6x^2+12x

2x(x^2-1)=2x^3-2x