Question

descompuneti in factori:
(x+1)³-(x-2)³

Answer 1

Răspuns:

9·(x²-x+1)

Explicație pas cu pas:

(x+1)³-(x-2)³ = ?

Notam :

x+1 = a ; x-2 = b

Folosim formula :

a³-b³ = (a-b)(a²+ab+b²)

Inlocuim in formula :

(x+1)³-(x-2)³ = (x+1-x+2)[(x+1)²+(x+1)(x-2)+(x-2)²] =

= 3·(x²+2x+1+x²-x-2+x²-4x+4) = 3·(3x²-3x+3) = 9·(x²-x+1)

(x+1)³-(x-2)³ =  9·(x²-x+1)