simplyfi each of the following [1/3a+2/3b]^3+1/3a-2/3b]^3 please send me step by step explanation
Answers
Answer:
Step-by-step explanation:
Given : [1/3a+2/3b]^3+1/3a-2/3b]^3
To find : Simplify
Solution:
(1/3a + 2/3b)³ + (1/3a - 2/3b)³
1st method using
(x + y)³ = x³ + y³ + 3xy(x + y)
(x - y)³ = x³ + y³ - 3xy(x - y)
= (1/3a)³ + (2/3b)³ + 3(1/3a)(2/3b)(1/3a + 2/3b) + (1/3a)³ - (2/3b)³ - 3(1/3a)(2/3b)(1/3a - 2/3b)
= 2 (1/3a)³ + 3(1/3a)(2/3b)(1/3a + 2/3b - 1/3a + 2/3b)
= 2/27a³ + (2/3ab)(4/3b)
= 2/27a³ + 8/9ab²
= (2/9a)( 1/3a² + 4/b²)
another method using
x³ + y³ = (x + y) (x² + y² - xy)
(1/3a + 2/3b + 1/3a - 2/3b )( 1/9a² + 4/9b² +4/9ab + 1/9a² + 4/9b² - 4/9ab - 1/9a² + 4/9b²)
= (2/3a) (1/9a² + 12/9b²)
= (2/3a) (1/9a² + 4/3b²)
= (2/9a)(1/3a² + 4/b²)
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