Factorize:
a³-3a²b+3ab²-b³+8
Answers
The algebraic expression is given as : a³ - 3a²b + 3ab² - b³ + 8
We can rewrite the given expression as :
= {(a)³ – (b)³ - 3ab (a - b)} + 8
In order to factorise the given algebraic expression we use the following Identity - a³ - b³ - 3ab (a - b) = (a - b)³.
Here a = (a) and b = (b) :
= (a - b)³ + 2³
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 = (a - b) and b = 2 :
= (a – b + 2) {(a - b)² + (2)² - 2(a - b)}
By using an identity , (a - b)² = (a² - 2ab + b²) :
= (a - b + 2)(a² - 2ab + b² + 4 - 2a + 2b)
= (a - b + 2)(a² - 2ab + b² - 2a + 2b + 4)
Hence, the factorization of an algebraic expression is (a - b + 2)(a² - 2ab + b² - 2a + 2b + 4).
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