Trovo difficoltà

Ciao,

ecco l'esercizio:

se hai bisogno di chiarimenti, scrivi pure.

saluti 🙂

Foto dritta!!!

(x + 1)^2 - (x + 2)^2 + ((x - 1)·(x + 1))·(x^2 - 1) + (x^2 - 1)·(- x^2 + 1)=

=(x^2 + 2·x + 1) - (x^2 + 4·x + 4) + (x^2 - 1)·(x^2 - 1) + (x^2 - 1)·(- x^2 + 1)=

=(x^2 + 2·x + 1) - (x^2 + 4·x + 4) + (x^2 - 1)·(x^2 - 1) + (- x^4 + 2·x^2 - 1)=

=(x^2 + 2·x + 1) - (x^2 + 4·x + 4) + (x^4 - 2·x^2 + 1) + (- x^4 + 2·x^2 - 1)=

=- 2·x - 3

prodotti notevoli : 

(x+1)^2 = (x^2+1+ 2*x)

(x^2-1) = (x+1)*(x-1)

(x^2+1+2*x) - (x^2+4+4*x) + (x^2-1)*(x^2-1) + (x^2-1)*(- x^2+1)

(x^2+1+2*x) - (x^2+4+ 4*x) + (x^2-1)*(x^2-1) + (-x^4-1+2*x^2)

(x^2+1+2*x) - (x^2+4+4*x) + (x^4+1-2*x^2) + (- x^4-1+2*x^2)

x^2 si semplifica 

(x^4+1-2*x^2) e (- x^4-1+2*x^2) si semplificano

-2*x - 3

=============================================================

$\small \left(x+1\right)^2- \left(x+2\right)^2+ \left(x-1\right) \left(x+1\right) \left(x^2-1\right)+ \left(x^2-1\right) \left(-x^2+1\right) = $

$\small = x^2+2x+1- \left(x^2+4x+4\right)+ \left(x^2-1\right) \left(x^2-1\right)+ \left(-x^4+x^2+x^2-1\right) = $

$\small = x^2+2x+1- x^2-4x-4+ x^4-x^2-x^2+1-x^4+2x^2-1 = $

$\small = \cancel{x^2}+2x+1\cancel{- x^2}-4x-4\cancel{+ x^4}\cancel{-2x^2}\cancel{+1}\cancel{-x^4}\cancel{+2x^2}\cancel{-1} = $

$\small = +2x+1-4x-4 = $

$\small = -2x-3 $

Prodotti notevoli....

(x + 1)^2 = x^2 + 2x + 1;   (x + 2)^2 = x^2 + 4x + 4;

(x - 1) * (x + 1) = x^2 - 1;

(x^2 - 1 ) * (x^2 - 1) = (x^2 - 1)^2; quadrato di binomio

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

Ciao.

==============================================================

$\small \left(a+2b\right)^2-\left(a-2b\right)^2+\left(4ab+1\right)^2-\left(4ab+1\right)\left(4ab-1\right) =$

$\small = a^2+4ab+4b^2-\left(a^2-4ab+4b^2\right)+16a^2b^2+8ab+1-\left(16a^2b^2-1\right) =$

$\small = a^2+4ab+4b^2-a^2+4ab-4b^2+16a^2b^2+8ab+1-16a^2b^2+1 =$

$\small = \cancel{a^2}+4ab\cancel{+4b^2}\cancel{-a^2}+4ab\cancel{-4b^2}\cancel{+16a^2b^2}+8ab+1\cancel{-16a^2b^2}+1 =$

$\small = +4ab+4ab+8ab+1+1 =$

$\small = 16ab+2 $

=========================================================

$\small \left(a-3b \right) \left(-a-3b \right) + \left(a-3b \right) \left(a+3b\right)+\left(a-3b\right)\left(3b-a\right)+a^2+9b^2= $

$\small = -a^2-3ab+3ab+9b^2+a^2+3ab-3ab -9b^2+3ab-a^2-9b^2+3ab+a^2+9b^2= $

$\small = \cancel{-a^2}\cancel{-3ab}\cancel{+3ab}\cancel{+9b^2}\cancel{+a^2}\cancel{+3ab}\cancel{-3ab}\cancel{ -9b^2}+3ab\cancel{-a^2}\cancel{-9b^2}+3ab\cancel{+a^2}\cancel{+9b^2} = $

$\small = +3ab+3ab= $

$\small = 6ab $