Factorise 8x^3+27y^3+z^3-18xyz
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The answer is (2x + 3y + z)(4x² + 9y² + z² − 6xy − 3yz − 2zx)
Explanation:
Writing a number or other mathematical object as the result of numerous factors—typically smaller or simpler objects of the same kind—is known as factorization or factoring in mathematics. For instance, the polynomial x² - 4 and the integer 15 can be factored using the formula 3 x 5.
Solution:
8x³ + 27y³ + z³ − 18xyz
using the formula, a³ +b³ +c³ −3abc=(a+b+c)(a² +b² +c² −ab−bc−ac)
= (2x)³ + (3y)³ + z³ − 3 × 2x × 3y× z
= (2x +3y + z) [(2x)² + (3y)²+ z² −2x × 3y − 3y × z − z × 2x]
= (2x + 3y + z)(4x² + 9y² + z² − 6xy − 3yz − 2zx)
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