f(x)= 3x³ - 18x +9
Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.
Identity I: (a + b)² = a² + 2ab + b²
Identity II: (a – b)² = a² – 2ab + b²
Identity III: a² – b²= (a + b)(a – b)
Identity IV: (x + a)(x + b) = x² + (a + b) x + ab
Identity V: (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
Identity VI: (a + b)³ = a³ + b³ + 3ab (a + b)
Identity VII: (a – b)³ = a³ – b³ – 3ab (a – b)
Identity VIII: a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)
f(x) = (3x + 6) (x - 3)²
= ( 3x + 6) ( x - 3 )²
= ( 3x + 6)( x² - 6x + 9)
= 3x( x² - 6x + 9) + 6( x² - 6x + 9)
= 3x³ - 6x² + 18x + 6x² - 36x +9
= 3x³ - 18x +9
To learn more about algebraic expansions, refer to brainly.com/question/4344214
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