Question

ajutati maaaaa ex 11​

Answer 1

Răspuns:

a) $2\sqrt{3} (x-3)^{3}$

b) $4\sqrt{7} (x+1)(x^{2} +2x+4)$

c) $2\sqrt{3} (x-\frac{1}{2} )^{3}$

d) $3\sqrt{5} (x+\frac{2}{3} )^{3}$

Explicație pas cu pas:

a)

$2\sqrt{3} x^{2} (x-3) - 12\sqrt{3} x(x-3) + 18\sqrt{3} (x-3)$

$= 2\sqrt{3} (x-3)(x^{2} - 6x+9)$  - am dat factor comun pe 2√3(x-3)

$= 2\sqrt{3} (x-3)(x-3)^{2}$ - am scris pe x²-6x+9 ca fiind (x-3)²

$= 2\sqrt{3} (x-3)^{3}$

b)

$4\sqrt{7} x^{2} (x+1) + 8\sqrt{7} x(x+1) + 16\sqrt{7} (x+1)$

$= 4\sqrt{7} (x+1)(x^{2} +2x+4)$

c)

$4\sqrt{3} x^{2} (2x-1)-4\sqrt{3} x (2x-1) +\sqrt{3} (2x-1)$

$= \sqrt{3} (2x-1)(4x^{2} -4x+1)$  

$= \sqrt{3} (2x-1)(x-\frac{1}{2} )^{2}$

$= 2\sqrt{3} (x-\frac{1}{2} )(x-\frac{1}{2} )^{2}$

$= 2\sqrt{3} (x-\frac{1}{2} )^{3}$

d)

$9\sqrt{5} x^{2} (3x+2)+12\sqrt{5} x(3x+2)+4\sqrt{5} (3x+2)$

$= \sqrt{5} (3x+2)(9x^{2} +12x+4)$

$= \sqrt{5} (3x+2)(x+\frac{2}{3} )^{2}$

$= 3\sqrt{5} (x+\frac{2}{3} )(x+\frac{2}{3} )^{2}$

$= 3\sqrt{5} (x+\frac{2}{3} )^{3}$