Question

1)Descompus in produs de factori:
( 4x+1)^2 - (2x+3)^2 este ..

Answer 1

$Sa~notam~4x+1=a~si~2x+3=b. \\ \\ (4x+1)^2-(2x+3)^2= \\ =a^2-b^2= \\ =(a+b)(a-b)= \\ =[(4x+1)+(2x+3)][(4x+1)-(2x+3)]= \\ =(4x+1+2x+3)(4x+1-2x-3)= \\ =(6x+4)(2x-2) =\\ =2(3x+2) \cdot 2(x-1)= \\ =\boxed{4(3x+2)(x-1)}$

Answer 2

(4x+1)²-(2x+3)²=
16x²+1+8x-(4x²+9+12x)=
16x²+8x+1-4x²-12x-9=
12x²-4x-8=4(3x²-x-2)
3x²-x-2=3x²-3x+2x-2
3x(x-1)+2(x-1)=(3x+2)(x-1) deci rezultatul va fi 4(3x+2)(x-1)