Factorize each of the following expressions:
8x³+27y³-216z³+108xyz
Answers
Answer:
Using Identity x^3 + y^3 + z^3 -3xyz
The algebraic expression is given as: 8x³ + 27y³ - 216z³ + 108xyz
We can rewrite the given expression as :
= (2x)³ + (3y)³ + (- 6z)³ − 3 × 2x × (3y)(- 6z)
In order to factorise the given algebraic expression of the form a³ + b³ + c³ - 3abc , we use the following Identity -: a³ + b³ + c³ - 3abc = (a + b + c) (a² + b³ + c² - ab - bc - ca) :
= {(2x + 3y - 6z)}{(2x)² + (3y)² + (-6z)² − 2x(3y) − (3y)(-6z) −(-6z)(2x)}
= (2x + 3y - 6z)(4x² + 9y² + 36z² - 6xy + 18yz + 12zx)
Hence, the factorization of an algebraic expression is (2x + 3y - 6z)(4x² + 9y² + 36z² - 6xy + 18yz + 12zx).
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