\(=\left(x^2-6x+9\right)-2=\left(x-3\right)^2-\sqrt{2^2}=\left(x-3-\sqrt{2}\right)\left(x-3+\sqrt{2}\right)\)

?

(x-4)*(x+3)

Phân tích đa thức thành nhân tử

\(x^2-x-12=x^2-x-9-3\)

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

\(=\left(x-3\right).\left(x+3\right)-\left(x+3\right)\)

\(=\left(x+3\right).\left(x-4\right)\)

\(=2\left[\left(x-3\right)^2-\dfrac{1}{16}\left(x-1\right)^2\right]\\ =2\left(x-3-\dfrac{1}{4}x+\dfrac{1}{4}\right)\left(x-3+\dfrac{1}{4}x-\dfrac{1}{4}\right)\\ =2\left(\dfrac{3}{4}x-\dfrac{11}{4}\right)\left(\dfrac{5}{4}x-\dfrac{13}{4}\right)\)

a) x⁴ + 3x³ - 7x² - 27x - 18

= x⁴ + x³ + 2x³ + 2x² - 9x² - 9x - 18x - 18

= x³ . (x + 1) + 2x² . (x + 1) - 9x . (x + 1) - 18(x + 1)

= (x + 1)(x³ + 2x² - 9x - 18)

= (x + 1)[x² .(x + 2) - 9.(x + 2)]

= (x + 1)(x + 2)(x² - 3²)

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

b) x⁴ + 3x³ + 3x² + 3x + 2

= x⁴ + x³ + 2x³ + 2x² + x² + x + 2x + 2

= x³ (x + 1) + 2x² . (x + 1) + x(x + 1) + 2(x + 1)

= (x + 1)(x³ + 2x² + x + 2)

= (x + 1)[x² .(x + 2) + (x + 2)]

= (x + 1)(x + 2)(x² + 1)

\(x^4+3x^3-7x^2-27x-18\)

\(=\left(x^4+x^3\right)+\left(2x^3+2x^2\right)-\left(9x^2+9x\right)-\left(18x-18\right)\)

\(=x^3\left(x+1\right)+2x^2\left(x+1\right)-9x\left(x+1\right)-18\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3+2x^2-9x-18\right)\)

\(=\left(x+1\right)\left[\left(x^3-3x^2\right)+\left(5x^2-15x\right)+\left(6x-18\right)\right]\)

\(=\left(x+1\right)\left[x^2\left(x-3\right)+5x^2\left(x-3\right)+6\left(x-3\right)\right]\)

\(=\left(x+1\right)\left(x-3\right)\left(x^2+5x+6\right)\)

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

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

đề sai rồi nhé

a, \(\dfrac{x^2}{4}-xy+y^2=\left(\dfrac{x}{2}\right)^2-xy+y^2=\left(\dfrac{x}{2}\right)^2-2.\dfrac{x}{2}.y+y^2\)

\(=\left(\dfrac{x^2}{2}-y\right)^2\)

b, \(x^2+x+\dfrac{1}{4}=x^2+\dfrac{1}{2}.2.x+\left(\dfrac{1}{2}\right)^2=\left(x+\dfrac{1}{2}\right)^2\)

c, \(x^2+2\sqrt{3}x+3=x^2+2\sqrt{3}x+\left(\sqrt{3}\right)^2=\left(x+\sqrt{3}\right)^2\)

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

`x^2/4-2*x/2*y+y^2`

`=(x/2-y)^2`

`x^2+x+1/4`

`=x^2+2*x*1/2+(1/2)^2`

`=(x+1/2)^2`

`x^2+2sqrt3x+3`

`=x+2xsqrt3+sqrt3^2`

`=(x+sqrt3)^2`

`4x^2-1`

`=(2x)^2-1`

`=(2x-1)(2x+1)`

\(=x^2-\left(y-4\right)^2\)

\(=\left(x-y+4\right)\left(x+y-4\right)\)

\(=x^2-\left(y^2-8y+16\right)=x^2-\left(y-4\right)^2=\left(x-y+4\right)\left(x+y-4\right)\)

a: =5(2x+3y)

d: =(x+1-y)(x+1+y)