factorize:27x^3+8x^3+1

Dear student,

Its (3x)^3+(2x)^3+1^3

use the expansion for a3+b3+c3

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Askiitians Expert

Sagar Singh

B.Tech, IIT Delhi

27 x^3 + 8 x^3 + 1

= 35 x^3 + 1

a³ + b³  = (a + b)(a² – ab + b²)

so

35 x^3 + 1 = (35x + 1 ) ( 35 x^2 - 35 x + 1)

 Solving the (35x^2 - 35x + 1) as quadratic equation)

 roots are 35 + sqrt(1085) and 35 - sqrt(1085)

35x+1 = 0 ----------

==> x = -1/2

therefore roots are

x = -1/2

x = 35 + sqrt (1085)

x = 35 - sqrt (1085)

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pleaSE tell me the identity of a^3+b^3+c^3