Question

The second term of the expansion of (3x + 2)^4 is:

Answer 1

Question:

• To find the second term of the expansion of (3x + 2)^4 .

Solution:

First of all we have to expand the expansion,

We can expand it in 2 ways:

• Using binomial theorem
• Using formula $\sf (x+y)^4$

Expanding using formula:

$\red\bigstar\; \large \boxed{\sf (a+b)^4 = a^4+4a^3b+6a^2b^2+4ab^3+b^4}$

Here,

• a = 3x
• b = 2

Putting the values,

$\sf\implies (3x+2)^4 =(3x)^4+4(3x)^3(2)+6(3x)^2(2)^2+4(3x)(2)^3+(2)^4 \\\\\sf\implies (3x+2)^4 =81x^4 +216x^3+216x^2+96x+16$

Expanding using binomial :

$\sf\implies(3x+2)^4 =\sf ^4C_0\;x^4y^0+ ^4C_1x^{(4-1)}y^1+ ^4C_2x^{(4-2)}y^2+ ^4C_3x^{(4-3)}y^3+ ^4C_4x^{(4-4)}y^4\\\\\sf\implies(3x+2)^4 =^4C_0x^4y^0+ ^4C_1x^{3}y^1+ ^4C_2x^{2}y^2+ ^4C_3xy^3+ ^4C_4y^4$

$\red\bigstar\;\boxed{\sf ^n C_r = \dfrac{n{\displaystyle !\,}}{{\displaystyle (n-r)!\,\displaystyle r!\,}}}$

or we can find $\sf ^n C_r$ using parscal's triangle,provided in attachment.

So,

$\sf\implies(3x+2)^4 =81x^4 +216x^3+216x^2+96x+16$

Therefore,

2nd term of expansion of $\sf (3x + 2)^4 \;is \;216x^3$

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