Factorize each of the following expressions:
x³y³+1
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The algebraic expression is given as : x³y³ + 1
= (xy)³ + 1³
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 = (xy) and b = (1) :
= (xy + 1) ((xy)² - xy × 1 + 1²)
= (xy + 1) (x²y² - xy + 1)
Hence, the factorization of an algebraic expression is (xy + 1) (x²y² - xy + 1).
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