Question

(3x+4)^2-(x+5)^2
(2x+1)^2-(x-1)^2
(3x+2)^2-(2x+1)
Descompuneti in factori

Answer 1

(3x+4)²-(x+5)²=( 3x+4+x+5)(3x+4-x-5)=(4x+9)(2x-1)
(2x+1)²-(x-1)²= (2x+1+x-1)(2x+1-x+1)=3x(x+2)
(3x+2)²-(2x+1)²=(3x+2+2x+1)(3x+2-2x-1)=(5x+6)(x+1)

Se aplica : a² -b²= (a+b)× (a-b)

Answer 2

a)   (3x+4)²-(x+5)²=9x²+24x+16-(x²+10x+25)=9x²+24x+16-x²-10x-25=8x²+14x-9=8x²+18x-4x-9=2x(4x+9)-(4x+9)=(4x+9)(2x-1)
b)  (2x+1)²-(x-1)²=(2x+1+x-1)(2x+1-x+1)=3x(x+2)
c)  (3x+2)²-(2x+1)=9x²+12x+4-(4x²+4x+1)=9x²+12x+4-4x²-4x-1=5x²+8x+3=5x²+5x+3x+3=5x(x+1)+3(x+1)=(x+1)(5x+3)