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Factorization of Cubic PolynomialCovid19 has led the world to go through a phenomenal transition . Elearning is the future today. Stay Home , Stay Safe and keep learning!!! In this section, we will discuss Factorization of Cubic Polynomial.The degree of the cubic (highest exponent) polynomial is 3. There are different identities in Factorization of Cubic Polynomial . They are as follows : 1) a^{3} + b^{3} + 3a^{2}b + 3b^{2}a = (a + b)^{3} 2) a^{3}  b^{3}  3a^{2}b + 3b^{2}a = (a  b)^{3} 3) a^{3} + b^{3} = (a + b)(a^{2}  ab + b^{2}) 4) a^{3} b^{3} = (a  b)(a^{2} + ab + b^{2}) 5) a^{3} + b^{3}+ c^{3} 3abc = (a + b + c)(a^{2} + b^{2}+ c^{2}  ab  bc  ac) 6) If a + b + c = 0 then a^{3} + b^{3}+ c^{3}=3abc Using Identities Examples : 1)27x ^{3}  8 Solution : As first term and the 2nd term are perfect cube, we use the identity of cube
a = 3x and b = 2 27x ^{3}  8 = (3x 2)[(3x) ^{2} + 6x + 2 ^{2} )] = (3x 2)(9x ^{2} + 6x + 4)are the factors. ________________________________________________________________ 2) 8x ^{3} +1 Solution : As first term and the 2nd term are perfect cube, we use the identity of cube
a = 2x and b = 1 8x ^{3} + 1 = (2x + 1)[(2x) ^{2}  2x + 1 ^{2} )] = (2x +1 )(4x ^{2}  2x + 1)are the factors. ________________________________________________________________ 3) 27x ^{3} + y ^{3} + 9x ^{2} y + 3xy ^{2} Solution : As in the given equation there are two perfect cubes, so we can use 1st identity. 27x ^{3} + y ^{3} + 27x ^{2} y + 9xy ^{2} = (3x) ^{3} + (y) ^{3} + 3(3x) ^{2} y + 3(3x)y ^{2} = (3x + y) ^{3} [ here a = 3x and b= y;a ^{3} + b ^{3} + 3a ^{2} b + 3b ^{2} a = (a + b) ^{3} ] _______________________________________________________________ 4) (1.5) ^{3}  (0.9) ^{3}  (0.6) ^{3} Solution : (1.5) ^{3}  (0.9) ^{3} + (0.6) ^{3} Let a = 1.5, b =  0.9 and c = 0.6 As a + b + c = 1.5 + 0.9  0.6 = 0 a ^{3} + b ^{3} + c ^{3} = 3abc = 3(1.5)( 0.9)(0.6) = 2.430 Factoring • Factorization by common factor • Factorization by Grouping • Factorization using Identities • Factorization of Cubic Polynomial • Solved Examples on Factorization Covid19 has affected physical interactions between people. Don't let it affect your learning.
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