Question

1) Doprowadź do najprostszej postaci:

a) (a-1)(a+1)+(a+1)²-(a-1)²-a(a-1) =

b) (x+2y([5(x+2y)²-3(2x-y)²-5(x²-y²-x+3y]-1 =

Proszę o szybkie rozwiązanie zadania ;)

Answer 1

a) a(do kwadratu)+a-a-1+a(do kwadratu)+a+1+a-a(do kwadratu)+a=a(do kwadratu)+3a

Answer 2

a) (a-1)(a+1)+(a+1)²-(a-1)²-a(a-1) = a^{2} - 1 + a^{2}-2a+1 - a^{2}-a = a^{2}-3a

 

b) (x+2y([5(x+2y)²-3(2x-y)²-5(x²-y²-x+3y]-1 =

(x+2y[5(x^{2}+4xy+4y^{2})-3(4x^{2}-4xy+y^{2})-5x^{2}+5y^{2}+5x-15y]-1 =

(x+2y[5x^{2}+20xy+20y^{2}-12x^{2}+12xy-3y^{2}-5x^{2}+5y^{2}+5x-15y]-1 =

(x+2y[-12x^{2}+24xy+22y^{2}+5x-15y]-1=

-12x^{3}+24x^{2}y+22y^{3}+5x^{2}-15xy-24x^{2}y+48xy^{2}+44y^{3}+10xy-30y^{2} =

-12x^{3}+66y^{3}+5x^{2}-30y^{2}-5xy+48xy^{2}-1