4. Factorize the expression: p? + 27
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The algebraic expression is given as: p³ + 27
= (p)³ + (3)³
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 = p and b = 3
= (p + 3) (p² - 3p + 3²)
= (p + 3) (p² - 3p + 9)
Hence, the factorization of an algebraic expression is (p + 3) (p² - 3p + 9).
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