Question

Descompus in produs de factori :
a) (4x+1)*--(2x+3)* este....
b) x*--y*+8x+16 este.....
c)25x*--(2x+1)* este.....
d) x*+2xy+y*-8lt* este.....???

Answer 1

$a)(4x+1)^2 -(2x+3)^2 =[(4x+1)-(2x+3)][(4x+1)+(2x+3)]= \\ \\ =(4x+1-2x-3)(4x+1+2x+3)= \\ \\ =(2x-2)(6x+4) = \\ \\ \boxed{2(x-1)(3x+2)}$

$b)x^2 -y^2+8x+16= x^2 -(y^2+8x+16)= \\ \\ =x^2-(y+4)^2 = \\ \\ =[x-(y+4)][x+(y+4)]= \\ \\ =\boxed{(x-y-4)(x+y+4)}$

$c)25x^2-(2x+1)^2 =[25-(2x+1)][25+(2x+1)]= \\ \\ =(25-2x-1)(25+2x+1)= \\ \\ =(24-2x)(26+2x)= \\ \\ =\boxed{2(12-x)(13+x)}$

$d)x^2+2xy+y^2-81t^2= (x^2+2xy+y^2)-81t^2= \\ \\= (x+y)^2 -81t^2 = \\ \\ =[(x+y)-9t][(x+y)+9t]= \\ \\ =\boxed{(x+y-9t)(x+y+9t)}$