35 – a3 + 6a2 – 12a
(FATORISE)
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Answer:
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Given : 35 – a³ + 6a² – 12a
To Find : Factorize
Solution:
35 – a³ + 6a² – 12a
= 27 + 8 - a³ + 6a² – 12a
= 27 - ( -8 + a³ - 6a² + 12a)
= 27 - ( a³ - 6a² + 12a - 8)
= 27 - ( a³ + 3a²(-2) + 3a(-2)² + (-2)³ )
( x + y)³ = x³ + 3x²y + 3xy² + y³
x = a and y = -2
= 27 - ( a - 2)³
= 3³ - (a - 2)³
x³ - y³ = (x - y) (x² + y² + xy)
= ( 3 - (a - 2) ) ( 3² + (a - 2)² + 3(a - 2))
= ( 5 - a) ( 9 + a² - 4a + 4 + 3a - 6)
= (5 - a) ( a² - a + 7)
35 – a³ + 6a² – 12a = (5 - a) ( a² - a + 7)
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