Question

Descompunere in produs de factori : (4×+1) la a-2 putere - (2×+3) la a 2......

Answer 1

$(4x+1)^2-(2x+3)^2= \\ \\ = \big [(4x+1)+(2x+3) \big] \big [(4x+1)-(2x+3) \big]= \\ \\ =(4x+1+2x+3)(4x+1-2x-3)= \\ \\ =(6x+4)(2x-2)= \\ \\ =2(3x+2)2(x-1)= \\ \\ =4(3x+2)(x-1).$

Answer 2

(4x+1)²-(2x+3)²=
16x²+8x+1-(4x²+12x+9)=
16x²-4x²+8x-12x+1-9=
12x²-4x-8=0         :4
3x²-x-2=0
Δ=1+24=25
x1=(1-5)/6=-4/6=-2/3
x2=(1+5)/6=6/6=1
(4x+1)²-(2x+3)²=(x+2/3)(x-1)=(3x+2)(x-1)