Question

Find the expansion $(3x^2-2ax+3a^2{)}^3$ using binomial theorem.

Answer 1

For binomial expansion first let's do a small pairing inside the bracket

${[{3x}^2-a(2x-3a\left)\right]}^3$

Now let's expand this as be normally do for two digit expansion.

${[{3x}^2-a(2x-3a\left)\right]}^3={{(3x}^2)}^3-3C_1{{(3x}^2)}^2.a(2x-3a)+3C_2{{(3x}^2)}^{}.a^2(2x-3a){}^2-a^3(2x-3a){}^3$

${27x}^6-54x^{5}a+81a^2{x}^4-108a^3{x}^3+81a^4{x}^3-8a^3{x}^3+36a^4{x}^2-54a^5{x}^{}+27a^6$

${27x}^6-54x^{5}a+117a^2{x}^4-116a^3{x}^3+117a^4{x}^3-54a^5{x}^{}+27a^6$