Question

Descompuneti in factori: (lectia se numeste metode de calcul combinat)
$A) ( x^{2} +2x+1)-( y^{2} -4y+4) \\ B)9 a^{2} -(x^2-6x+9) \\ C)x^2-12x+36-y^2-2yz-z^2 \\ D)x^2+2 \sqrt{5} x+5-(y^2-2 \sqrt{2} y+2) \\ Multumesc frumos!$

Answer 1

A) = (x+1)² - (y-2)² = (x+1+y-2)(x+1-y+2)= (x+y-1)(x-y+3)
B) = 9a²- (x-3)² = (3a-x+3)(3a +x-3)
C) = (x-6)² - (y²+2yz+z²) = (x-6)² - (y+z)² = (x-6-y-z)(x-6+y+z)=(x-y-z-6)(x+y+z-6)
D) =(x+√5)² - (y-√2)² = (x+√5 -y+√2)(x+√5+y -√2) =(x-y+√5+√2)(x+y +√5-√2)