Question

Descompuneti in factori: c) 16(x+5)^2-9(2x-3)^2. d) 25x^4-4(x^2+2x-3)^2 e) 4x^2-9-(2x+3) f) (2x^2-2x+5)^2-(x^2+2x+2)^2. g) 4x^2-(x^2-2x+3)^2... Va rog,. Multumesc!

Answer 1

c)16(x+5)^2-9(2x-3)^2=
=[4(x+5)-3(2x-3)][4(x+5)+3(2x-3)]=
=(4x+20-6x+9)(4x+20+6x-9)=
=(-2x+29)(10+11)


d) 25x^4-4(x^2+2x-3)^2 =
=[5x^2-2(x^2+2x-3)][5x^2+2(x^2+2x-3)]=
=[5x^2-2x^2-4x+6)(5x^2+2x^2+4x-6)=
=[3x^2-4x+6)(7x^2+4x-6)


e) 4x^2-9-(2x+3) =
=(2x-3)(2x+3)-(2x+3)= (2x+3)(2x-3-1)=(2x+3)(2x-4)=2(2x+3)(x-2)


 f) (2x^2-2x+5)^2-(x^2+2x+2)^2
=(2x^2-2x+5-x^2-2x-2)(2x^2-2x+5+x^2+2x+2)=
=(x^2-4x+3)(3x^2+7)=(x^2-x-3x+3)(3x^2+7)=[x(x-3)-(x-3)](3x^2+7)=
=(x-3)(x-1)(3x^2+7)

 g) 4x^2-(x^2-2x+3)^2=(2x-x^2+2x-3)(2x+x^2-2x+3)=(4x-x^2-3)(x^2+3)=
=-(x^2-4x+3)(x^2+3)=(x-3)(x-1)(x^2+3)