Question

разложите на множители
а)125a^3-8b^3
б)a^3+27b^3
в)x^6-a^6

Answer 1

a) 125a³-8b³=(5a)³-(2b)³=(5a-2b)((5a)²+5a×2b+(2b)²)=(5a-2b)(25a²+10ab+4b²)
б) a³+27b³=a³+(3b)³=(a+3b)(a²-a×3b+(3b)²)=(a+3b)(a²-3ab+9b²)
в) x^6-a^6=(x²)³-(a²)³=(x²-a²)((x²)²+x²a²+(a²)²)=(x²-a²)(x⁴+x²a²+a⁴)=(x-a)(x+a)(x⁴+x²a²+a⁴)

Answer 2

а)125a³-8b³ = (5а)³ - (2b)³ = (5а-2b)((5а)²+5a·2b+(2b)²) =
= (5а-2b)(25а²+10ab+4b²)  


б) a³+27b³ =  (а)³ + (3b)³ = (а+3b)(а²-a·3b+(3b)²) = 
= (а+3b)(а²-3ab+9b²)  

в) x⁶-a⁶ =  (x²)³ - (a²)³ = (x²-a²)((x²)²+x²·a²+(a²)²) = 
= (x-a)(x+a)(x⁴+a²x²+a⁴)