Question

a.)descompunerea in factori a expresiei x^2+x=
b)descompunerea in factori a expresiei x^2-4=
c.)descompunerea in factori a expresiei(x+y+1)^2-(x-y+1)^2+=
DAU CORONITA!!!!!!!!!!!!!!!!!!!!!!!

Answer 1

a) x²+x=x(x+1)

b) x²-4=(x+2)(x-2)

c)  (a+b+c)²=(a+b+c)(a+b+c)=a²+ab+ac-ab +b²+bc+ac+bc+c²=
=a²+b²+c²+2ab+2bc+2ac

(a-b+c)²=(a-b+c)(a-b+c)=a²-ab+ac-ab +b²-bc+ac-bc+c²
=a²+b²+c²-2ab-2bc+2ac


(x+y+1)²-(x-y+1)²=[x²+y²+1+2xy+2x+2y]-[x²+y²+1-2xy-2x+2y]=4xy+4x
=4x(y+1)

Answer 2

a) x² + x = x(x+1) 

b) x² - 4 = x² - 2² = (x-2)(x+2) 

c) ( x + y + 1 )² - ( x - y + 1 )² = 
= ( x + y + 1 - ( x - y + 1 ))( x + y + 1 + ( x - y + 1 )) =
= ( x + y+ 1 - x + y - 1)( x + y + 1 + x -y + 1 ) =
= 2y(2x+2) = 2y × 2(x+1) = 2 × 2y(x+1) = 4y(x+1)