Factorize each of the following expressions:
32a²+108b³
Answers
The algebraic expression is given as : 32a³ + 108b³
Taking 4 as common :
= 4 (8a³ + 27b³)
= 4 (2a)³ + (3b³)
In order to factorise the given algebraic expression as the sum of two cubes we use the following identities - a³ + b³ = (a + b) (a² - ab + b²) :
Here a = 2a and b = 3b :
= 4 (2a + 3b) ((2a)² - 2a × 3b + (3b)²)
= 4 (2a + 3b) (4a² - 6ab + 9b²)
Hence, the factorization of an algebraic expression is 4 (2a + 3b) (4a² - 6ab + 9b²).
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Answer:
Step-by-step explanation:
Taking 4 as common :
= 4 (8a³ + 27b³)
= 4 (2a)³ + (3b³)
Here a = 2a and b = 3b :
= 4 (2a + 3b) ((2a)² - 2a × 3b + (3b)²)
= 4 (2a + 3b) (4a² - 6ab + 9b²)