Question

Va rog sa explicați.

Answer 1

Pt. prima paranteza aplicam formula (a+b+c)² = a²+b²+c²+2ab+2ac+2bc, unde, in cazul nostru, a = x², b = x si c = 1.

(x²+x+1)² = (x²)²+x²+1² + 2·x²·x + 2·x²·1 + 2·x·1 = x^4 + x² + 1 + 2x³ + 2x² + 2x = x^4 + 3x² + 2x³ + 2x + 1

Pt. a doua paranteza aplicam formula (a+b)² = a²+2ab+b², unde, in cazul nostru, a=x² si b=2.

(x²+2)² = (x²)²+2·x²·2+2² = x^4 + 4x² + 4

=>

(x²+x+1)² - (x²+2)² - 2x = x^4 + 3x² + 2x³ + 2x + 1 - (x^4 + 4x² + 4) - 2x = x^4 + 3x² + 2x³ + 2x + 1 - x^4 - 4x² - 4 - 2x = x^4 - x^4 + 2x³ + 3x²-4x² +2x-2x + 1-4 = 0 + 2x³ - x² + 0 - 3 = 2x³-x²-3