Factorize each of the following expressions:
a³+b³+a+b
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The algebraic expression is given as: a³ + b³ + a + b
= (a³ + b³) + (a + b)
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) :
= (a + b) (a² + b² – ab) + a + b
a³ + b³ + a + b = (a + b)(a² + b² – ab + 1)
Hence, the factorisation of a³ + b³ + a + b is (a + b)(a² + b² – ab + 1).
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Answer:
Step-by-step explanation:
= (a³ + b³) + (a + b)
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) :
= (a + b) (a² + b² – ab) + a + b
a³ + b³ + a + b = (a + b)(a² + b² – ab + 1)
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