Question

factorize: (2a+1)^3 + (a-1)^3​

Answer 1

Step-by-step explanation:

a^3 + b^3 = (a+b)(a^2-ab+b^2)

using this identity

= (2a+1+a-1)((2a+1)^2-(2a+1)(a-1)+(a-1)^2)

= 3a(4a^2 + 1+4a-2a^2+2a+a-1+a^2+1-2a)

= 3a(a^2 +5a +1)

now let's factorize a^2+5a+1

by using Shree Dhracharya Formula

$\frac{ - 5( + - ) \sqrt{25 - 4} }{2} \\ = \frac{ - 5 + \sqrt{21} }{2} \: \: \: and \frac{ - 5 - \sqrt{21} }{2}$

so the factor of given eqn are

$3a(a - ( \frac{ - 5 + \sqrt{21} }{2} ))(a - (\frac{ - 5 - \sqrt{21} }{2} ))$

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