(Math Quiz 10 – CT) In the expansion ({left( {8{a^2} – frac{1}{2}b} right)^6}), the coefficient of the containing term ({a^9 }{b^3}) is:

• Question:

In the expansion $${\left( {8{a^2} – \frac{1}{2}b} \right)^6}$$, the coefficient of the term contains $${a^9}{ b^3}$$ is:

Reference explanation:

$${T_{k + 1}} = {\left( { – 1} \right)^k}C_6^k{.8^{6 – k}}{a^{12 – 2k}}{.2 ^{ – k}}{b^k}$$.
Then the coefficient of the term containing $${a^9}{b^3}$$ is: $$– 1280{a^9}. {b^3}$$.