Identitats notables

Utilitzant identitats notables desenvolupa les següents expressions algebraiques:

  1. $(x+y+1)^2$
  2. $(x+1)\cdot(x-1)\cdot(x-1)\cdot(x+1)$
  3. $(x^2-2)^3$

$$(x+y+1)^2=(x+(y+1))^2=x^2+2\cdot x\cdot(y+1)+(y+1)^2=$$

$$=x^2+2xy+2x+(y^2+2y+1)=x^2+y^2+2xy+2x+2y+1$$

$$(x+1)\cdot(x-1)\cdot(x-1)\cdot(x+1)=$$

$$=((x+1)\cdot(x-1))\cdot((x-1)\cdot(x+1))=$$

$$=(x^2-1)\cdot(x^2-1)=(x^2-1)^2=x^4-2x^2+1$$

$$(x^2-2)^3=(x^2)^3-3\cdot(x^2)^2\cdot2+3\cdot x^2\cdot 2^2-2^3=x^6-6x^4+12x^2-8$$

  1. $x^2+y^2+2xy+2x+2y+1$
  2. $x^4-2x^2+1$
  3. $x^6-6x^4+12x^2-8$
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