Question

Descompuneti in produs de factori: a) $(x+2)^{2}$ b)(2x-1)²-x² c) (3x+2)²-25x² d)(8x-3)²-(2x+5)² e)(4x+1)²-(x²-4x)² f)4x²-(x²-5x)²

Answer 1

   
[tex]\displaystyle\\ a) (x+2)^2= (x+2)(x+2) \\\\ b)(2x-1)^2-x^2=(2x-1-x)(2x-1+x)=(x-1)(3x-1) \\\\ c) (3x+2)^2-25x^2= (3x+2-5x)(3x+2+5x)=(2x+2)(8x+2)\\\\ d)(8x-3)^2-(2x+5)^2=(8x-3-(2x+5))(8x-3+(2x+5))=\\ =(8x-3-2x-5)(8x-3+2x+5)=(6x-8)(10x+2)\\\\ e)(4x+1)^2-(x^2-4x)^2=(4x+1-(x^2-4x))(4x+1+(x^2-4x))= \\ =(4x+1-x^2+4x)(4x+1+x^2-4x)=(-x^2+8x+1)(x^2+1) \\\\ f)4x^2-(x^2-5x)^2 =(2x-(x^2-5x))(2x+(x^2-5x))=\\ =(2x-x^2+5x)(2x+x^2-5x)=(7x-x^2)(-3x+x^2)=\\ =x(7-x) \times x(x-3)=x^2(7-x)(x-3)[/tex]