Question

Descompuneți în produs de factori (4x+1)^2-(2x+3)^2

Answer 1

$Folosim~formula~\boxed{A^2-B^2=(A+B)(A-B)}~pentru~A=4x+1 \\ \\ si~B=2x+3. \\ \\ (4x+1)^2-(2x+3)^2= \\ \\ =A^2-B^2= \\ \\ =(A+B)(A-B)= \\ \\ =\left((4x+1)+(2x+3) \right)\left( (4x+1)-(2x+3)\right)= \\ \\ =(4x+1+2x+3)(4x+1-2x-3)= \\ \\ =(6x+4)(2x-2)= \\ \\ =4(3x+2)(x-1).$