Question

Answer 1

a) x² - 6x + 9

= x² - 2.x.3 + 3²

= (x - 3)²

b) x² - 6

= x² - (√6)²

= (x - √6)(x + √6)

c) 1 - 27x³

= 1³ - (3x)³

= (1 - 3x)(1 + 3x + 9x²)

d) x³ + 1/x³

= x³ + (1/x)³

= (x + 1/x)(x² - 1 + 1/x²)

e) -x³ + 9x² - 27x + 27

= -(x³ - 3.x².3 + 3.x.3² - 3³)

= -(x - 3)³

Answer 2

a)

\(x^2-6x+9=x^2-2.x.3+3^2\\ =\left(x-3\right)^2\)

b)

\(x^2-9\) mới đúng đề chứ 

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

Hoặc với `x^2-6` luôn nha:

\(x^2-6\\ =x^2-\left(\sqrt{6}\right)^2\\ =\left(x-\sqrt{6}\right)\left(x+\sqrt{6}\right)\)

c)

\(1-27x^3\\ =1-\left(3x\right)^3\\ =\left(1-3x\right)\left(1+3x+9x^2\right)\)

d)

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

e)

\(-x^2+9x^2-27x+27\\ =-\left(x^2-9x^2+27x-27\right)\\ =-\left(x^2-3.3x^2+3.3^2.x-3^3\right)\\ =-\left(x-3\right)^3\\ =-\left(x-3\right)\left(x-3\right)\left(x-3\right)\)