facyorize a3-27b3+2a^2b-6ab^2
Answers
Answered by
1
(a - 3b)(a² + 9b² + 5ab)
Step-by-step explanation:
→ a³ - 27b³ + 2a²b - 6ab²
→ (a)³ - (3b)³ + 2ab(a - 3b)
→ (a)³ - (3b)³ + 2ab(a - 3b)
From the identity a³ - b³ = (a - b)(a² + b² - ab)
→ (a - 3b)[a² + (3b)² + a(3b)] + 2ab(a - 3b)
→ (a - 3b)(a² + 9b² + 3ab)+ 2ab(a - 3b)
→ (a - 3b)[(a² + 9b² + 3ab) + 2ab]
→ (a - 3b)(a² + 9b² + 5ab)
Answered by
1
Answer:
(a-3b) [a^2+5ab+9b^2]
Step-by-step explanation:
know that
a^3 - b^3 = (a-b) (a^2 = ab = b^2) (1)
a^3 -27b^3 + 2a^b - 6ab^2
=(a)^3 - (3b) ^3 + 2ab (a-3b)
=(a-3b) [a^2+a x a 3b + (3b) + (3b) ^2] + 2ab (a - 3b) from (1)
=(a-3b) [a^2+3ab + 9b^2] + 2ab (a-3b)
=(a-3b) [a^2+3ab + 9b^2 + 2ab]
=(a-3b) [a^2+ 5ab + 9b^2]
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