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20. If a^4 a^2 b^2 b^4 8 and a^2 abb^2 4 , find the value of (i) a^2 b^2 ,(ii)ab.
    3 ⋅3 Formulae of Cubes
    Formula 6.(ab)^3 a^3  3 a^2 b 3 ab^2 b^3

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

Proof : (ab)^3 (ab)(ab)^2

=(ab)(a^2  2 abb^2 )

=a(a^2  2 abb^2 )b(a^2  2 abb^2 )

=a^3  2 a^2 bab^2 a^2 b 2 ab^2 b^3

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

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

Corollary 9.a^3 b^3 (ab)^3  3 ab(ab)

Formula 7.(ab)^3 a^3  3 a^2 b 3 ab^2 b^3

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

Proof :(ab)^3 (ab)(ab)^2

=(ab)(a^2  2 abb^2 )
=a(a^2  2 abb^2 )b(a^2  2 abb^2 )
=a^3  2 a^2 bab^2 a^2 b 2 ab^2 b^3
=a^3  3 a^2 b 3 ab^2 b^3
=a^3 b^3  3 ab(ab)
Observe : Substituting b instead of b in formula 6, we get formula 7 :

{a(b)}^3 a^3 (b)^3  3 a(b){a(b)}

That is, (ab)^3 a^3 b^3  3 ab(ab)

Corollary 10.a^3 b^3 (ab)^3  3 ab(ab)

Formula 8.a^3 b^3 (ab)(a^2 abb^2 )

Proof :a^3 b^3 (ab)^3  3 ab(ab)

=(ab){( ab)^2  3 ab}

=(ab)(a^2  2 abb^2  3 ab)

=(ab)(a^2 abb^2 )

Formula 9.a^3 b^3 (ab)(a^2 abb^2 )

Proof :a^3 b^3 (ab)^3  3 ab(ab)

=(ab){(ab)^2  3 ab}