Question

show that (a+b)³= a³+ b³+ 3ab(a+b)​

Answer 1

Answer:

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Step-by-step explanation:

(a+b)^3

= (a+b) (a+b) (a+b)

={(a+b) (a+b)} (a+b)

={a(a+b) + b(a+b)} (a+b)

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

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

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

=a^3 + a^2b + ab^2 + b^3 + 2a^2b + 2ab^2

=a^3 + b^3 + 3a^2b + 3ab^2

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

Now when we have expanded (a+b)^3 = a^3 + b^3 + 3ab(a+b)