Plsss answer I will mark as brilliant

(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

2 years ago

Helma wants to find the volume of the right rectangular prism shown below. Which equation could Helma use to find V, the volume

sleet_krkn [62]

V = 30*16*12. To find the volume of a rectangular prism, you just multiply the area of the base (side 1 * side 2) by the height of the prism.

5 0

2 years ago

Y=x^2 + 1 why is this function nonlinear?

ELEN [110]

Answer:

Its non linear because of the x squared. This would indicate an ever increasing answer, not one that has a constant rate. This equation would be quadratic.

7 0

2 years ago

The length of a rectangle is 3 more than its width. The perimeter of the rectangle is 58 cm. What are the rectangle’s dimensions

Alexeev081 [22]

Width = 13cm

Length = 16cm

<u>Explanation:</u>

Let width = b,

So, length = b+3

Perimeter of rectangle = 2x(length + width)

According to the question,

$58cm = 2X(b+3 + b)\\58cm = 2X(2b+3)\\29cm = 2b+3\\ 26cm = 2b\\b = 13cm$

Hence,

Width = 13cm

Length = 16cm

5 0

2 years ago

WILL GIVE BRAILIEST (06.02 MC)

Zarrin [17]

The second one is the correct answer

7 0

2 years ago

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