How many terms are in the expression: 12p + 8m + 2

(x +y)^5<br> Complete the polynomial operation

Vesna [10]

Answer:

Please check the explanation!

Step-by-step explanation:

Given the polynomial

$\left(x+y\right)^5$

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

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

$=\sum _{i=0}^5\binom{5}{i}x^{\left(5-i\right)}y^i$

so expanding summation

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

solving

$\frac{5!}{0!\left(5-0\right)!}x^5y^0$

$=1\cdot \frac{5!}{0!\left(5-0\right)!}x^5$

$=1\cdot \:1\cdot \:x^5$

$=x^5$

also solving

$=\frac{5!}{1!\left(5-1\right)!}x^4y$

$=\frac{5}{1!}x^4y$

$=\frac{5x^4y}{1}$

$=5x^4y$

similarly, the result of the remaining terms can be solved such as

$\frac{5!}{2!\left(5-2\right)!}x^3y^2=10x^3y^2$

$\frac{5!}{3!\left(5-3\right)!}x^2y^3=10x^2y^3$

$\frac{5!}{4!\left(5-4\right)!}x^1y^4=5xy^4$

$\frac{5!}{5!\left(5-5\right)!}x^0y^5=y^5$

so substituting all the solved results in the expression

$=\frac{5!}{0!\left(5-0\right)!}x^5y^0+\frac{5!}{1!\left(5-1\right)!}x^4y^1+\frac{5!}{2!\left(5-2\right)!}x^3y^2+\frac{5!}{3!\left(5-3\right)!}x^2y^3+\frac{5!}{4!\left(5-4\right)!}x^1y^4+\frac{5!}{5!\left(5-5\right)!}x^0y^5$

$=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

Therefore,

$\left(x\:+y\right)^5=x^5+5x^4y+10x^3y^2+10x^2y^3+5xy^4+y^5$

6 0

3 years ago

What is the difference between a defined and an undefined term in Geometry?

Flura [38]

The difference between defined and an undefined term in Geometry is that defined terms can be combined with each other or an undefined term, and by doing this, there is another term defined. For example, an angle is a combination of two rays, which is an undefined term. Undefined term on the other hand is used to define other terms.

6 0

3 years ago

Can someone please figure this out for me because I don't understand it.

lisabon 2012 [21]

The answer would be 'b'
Now, here Luke walks total 2¼ miles but his friend's home is ¼ mile. So, number of trips he makes = Total miles walked ÷ Distance to his friend's home
= 2¼ ÷ ¼ = 9

8 0

3 years ago

Please help me with these two questions if you can! Btw happy Tuesday

Ymorist [56]

Answer:

Happy Tuesday! Here i'll explain it:

Step-by-step explanation:

First you will have to make 2 2/5 into a improper fraction and then subtract the 5/6. after you have done that multiply the 3/4 to the number

7 0

3 years ago

0.2,-0.6,1/2,-2/3,5/8 in order from least to greatest using a number line

Neko [114]

Answer:

-2/3, -0.6, 0.2, 1/2, 5/8

Step-by-step explanation:

What you do is you have to make them into decimals.

-0.6 and 0.2 are already in decimals.

-2/3 as a decimal is -0.667

1/2 as a decimal is 0.5

5/8 as a decimal is 0.625

-2/3, -0.6, 0.2, 1/2, 5/8 is your answer.

8 0

3 years ago