Odpowiedź:
zad.4
( a + b ) ³ = a³ + 3×a²×b + 3×a×b² + b³
( a - b ) ³ = a³ - 3×a²×b + 3×a×b² - b³
(√2)³ = √2³ = √8 = √(4×2) = 2√2
(√2)² = √2² = √4 = 2
( √2 - 1 )³ + ( 2 + √2 )³ = (√2)³ - 3×(√2)²×1 + 3×√2×1² - 1³ + 2³ + 3×2²×√2 +
+ 3×2×(√2)² + (√2)³ = 2√2 - 3×2×1 + 3×√2×1 - 1 + 8 + 3×4×√2 + 3×2×2+2√2=
= 2√2 - 6 +3√2 - 1 + 8 + 12√2 + 12 + 2√2 = 16√2 + 13
zad.5
a)
u(x) = 2x³ - x² + 2x - 1
u(x) = x²×( 2x - 1 ) + 1×( 2x - 1 )
u(x) = ( 2x - 1 )×( x² + 1 )
