Question

Xpand the binomial (4x + 3y)3. The coefficient of the second term in the expansion of the binomial (4x + 3y)3 is .

Answer 1

Answer: 144

Step-by-step explanation:

The binomial is  $\left( 4x+3y\right)^3$

The expansion of $\Rightarrow \left ( a+b \right )^n=^nC_0\left ( a \right )^n\left ( b \right )^0+^nC_1\left ( a \right )^{n-1}\left ( b \right )^1+^nC_2\left ( a \right )^{n-2}\left ( b \right )^2+^nC_3\left ( a \right )^{n-3}\left ( b \right )^3+\ldots$

Expansion of $\left( 4x+3y\right)^3$

$\Rightarrow ^3C_0\left ( 4x\right )^{3}\left ( 3y\right )^0+^3C_1\left ( 4x\right )^{2}\left ( 3y\right )^1+^3C_2\left ( 4x\right )^{1}\left ( 3y\right )^2+^3C_3\left ( 4x\right )^{0}\left ( 3y\right )^3$

So, the second term is

$\Rightarrow ^3C_1\left ( 4x\right )^{3-1}\left ( 3y\right )^1\\\Rightarrow ^3C_1\left ( 4x\right )^{2}\left ( 3y\right )^1$

Its Coefficient is

$\Rightarrow ^3C_1\times 4^2\times 3\\\Rightarrow 3\times 16\times 3=144$