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What is the expansion of (3+x)^4

Vlad1618 [11]

Answer:

$\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81$

Step-by-step explanation:

Considering the expression

$\left(3+x\right)^4$

Lets determine the expansion of the expression

$\left(3+x\right)^4$

$\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i$

$a=3,\:\:b=x$

$=\sum _{i=0}^4\binom{4}{i}\cdot \:3^{\left(4-i\right)}x^i$

Expanding summation

$\binom{n}{i}=\frac{n!}{i!\left(n-i\right)!}$

$i=0\quad :\quad \frac{4!}{0!\left(4-0\right)!}3^4x^0$

$i=1\quad :\quad \frac{4!}{1!\left(4-1\right)!}3^3x^1$

$i=2\quad :\quad \frac{4!}{2!\left(4-2\right)!}3^2x^2$

$i=3\quad :\quad \frac{4!}{3!\left(4-3\right)!}3^1x^3$

$i=4\quad :\quad \frac{4!}{4!\left(4-4\right)!}3^0x^4$

$=\frac{4!}{0!\left(4-0\right)!}\cdot \:3^4x^0+\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1+\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2+\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3+\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4$

as

$\frac{4!}{0!\left(4-0\right)!}\cdot \:\:3^4x^0:\:\:\:\:\:\:81$

$\frac{4!}{1!\left(4-1\right)!}\cdot \:3^3x^1:\quad 108x$

$\frac{4!}{2!\left(4-2\right)!}\cdot \:3^2x^2:\quad 54x^2$

$\frac{4!}{3!\left(4-3\right)!}\cdot \:3^1x^3:\quad 12x^3$

$\frac{4!}{4!\left(4-4\right)!}\cdot \:3^0x^4:\quad x^4$

so equation becomes

$=81+108x+54x^2+12x^3+x^4$

$=x^4+12x^3+54x^2+108x+81$

Therefore,

$\left(3+x\right)^4:\quad x^4+12x^3+54x^2+108x+81$

6 0

3 years ago

3 1/3 (y+1 1/8 )=6 11/12 <br> hewp quickly

madam [21]

If you’re solving for y it’s 7/10

5 0

3 years ago

Read 2 more answers

8m/3 = 6/11 ?!?!?!?!?!?!?!?!?!?!?!?!!??!?!?!?!?!?!?!??!

GalinKa [24]

Answer:

cross multiply

(8m)(11)=(6)(3)

88m=18

then divide by 88 on both sides

m=18/88 then reduce by 2 -----> 9/44

Step-by-step explanation:

5 0

3 years ago

<img src="https://tex.z-dn.net/?f=%5Csqrt%7B-2%7D" id="TexFormula1" title="\sqrt{-2}" alt="\sqrt{-2}" align="absmiddle" class="l

kodGreya [7K]

Answer:

finding the square root of an negative number is not possible

5 0

3 years ago

If a= .75 and b= .50, what is the perimeter of the rectangle?

Lerok [7]

Answer:

C. 14 inches

Step-by-step explanation:

The perimeter is double the sum of length and width:

P = 2((4a +3) +(6b -2) = 8a +12b +2

For the given values, this is ...

P = 8(0.75) +12(0.50) +2 = 6 + 6 + 2 = 14

The perimeter is 14 inches.

3 0

3 years ago