To find: Expansion of (3x² – 2ax + 3a²)³

Formula used: (i)

(ii) (a+b)ⁿ =   ⁿC₀aⁿ + ⁿC₁a^n-1b + ⁿC₂a^n-2b² + …… +ⁿC_n-1ab^n-1 + ⁿC_nbⁿ

We have, (3x² – 2ax + 3a²)³

Let, (3x² – 2ax) = p … (i)

The equation becomes (p + 3a²)³

Substituting the value of p from eqn. (i)

… (ii)

We need the value of p³ and p², where p = 3x² – 2ax

For, (a+b)³ , we have formula a³+b³+3a²b+3ab²

For, (3x² – 2ax)³ , substituting a = 3x² and b = –2ax in the above formula

⇒ 27x⁶ – 8a³x³ – 54ax⁵ + 36a²x⁴ … (iii)

For, (a+b)² , we have formula a²+2ab+b²

For, (3x² – 2ax)³ , substituting a = 3x² and b = –2ax in the above formula

⇒ 9x⁴ – 12x³a + 4a²x² … (iv)

Putting the value obtained from eqn. (iii) and (iv) in eqn. (ii)

⇒ 27x⁶ – 8a³x³ – 54ax⁵ + 36a²x⁴ + 81a²x⁴ – 108x³a³ + 36a⁴x² + 81a⁴x² – 54a⁵x + 27a⁶

On rearranging

Ans) 27x⁶ – 54ax⁵ + 117a²x⁴ – 116x³a³ + 117a⁴x² – 54a⁵x + 27a⁶