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

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* 4^2* 3\\\Rightarrow 3* 16* 3=144`