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timama [110]
3 years ago
10

(x +y)^5 Complete the polynomial operation

Mathematics
1 answer:
Vesna [10]3 years ago
6 0

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{5}{1!}x^4y

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

=\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

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8 0
3 years ago
Ajax is 5 and 1 fourth feet tall. His sister is 3 eighths foot shorter than Ajax How tall is Ajax Sister?
user100 [1]

Answer:

4\frac{3}{4} feet tall

Step-by-step explanation:

Ajax is "5 and 1 fourth feet tall", which can be written as the mixed number 5\frac{1}{4} .

His sister is "3 eighths foot shorter", so she's 3/8 feet shorter than 5 1/4.

So, this is just a subtraction problem:

5\frac{1}{4} -\frac{3}{8}

To solve this, we want to convert 5 1/4 into an improper fraction, which is: \frac{21}{4} . Now, we want to find a common denominator. In this case, that common denominator is 8, so \frac{21}{4} =\frac{42}{8} .

Finally, we subtract 3/8 from 42/8: \frac{42}{8} -\frac{3}{8} =\frac{39}{8} . So, Ajax's sister is 39/8 feet. Converting this into a mixed number, we have: 39/8 = 4\frac{6}{8} =4\frac{3}{4} .

Therefore, Ajax's sister is 4\frac{3}{4} feet tall.

Hope this helps!

7 0
3 years ago
Read 2 more answers
Find the upper limit for the zeros of the function P(x)=4x^4+8x^3-7x^2-21x-9
pishuonlain [190]

Answer:

OPTION B - 2

Step-by-step explanation:

What is the upper limit for the zeros of the function P(x) = 4x^4 + 8x^3 - 7x^2 - 21x - 9. Ans: 2 is an upper limit. Use synthetic division. and the remainder are all positive, 2 is an upper limit.

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The distance between major cracks in a highway follows an exponential distribution with a mean of four miles. (a) what is the st
Lesechka [4]
For an exponential distribution, the standard deviation is equal to the mean.

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7 0
3 years ago
15x-7=2+12x I need help with this
Amanda [17]

Answer:

\huge{ \boxed{ \bold{ \tt{x = 3}}}}

<h3>♁ Question : Solve for x</h3>
  • 15x - 7 = 2 + 12x

<h3>♁ Step - by - step explanation</h3>
  • \text{15x - 7 = 2 + 12x}

Move 12x to L.H.S ( Left Hand Side ) and change it's sign

➛\sf{15x - 12x - 7 = 2}

Move 7 to R.H.S ( Right Hand Side) and change it's sign

➛\sf{15x - 12x = 2 + 7}

Subtract 12x from 15x

Remember that only coefficients of like terms can be added or subtracted.

➛\sf{3x = 2 + 7}

Add the numbers : 2 and 7

➛\sf{3x = 9}

Divide both sides by 3

➛ \sf{ \frac{3x}{3}  =  \frac{9}{3}}

➛ \boxed{ \bold{ \sf{x = 3}}}

The value of x is \boxed{ \sf{3}}

✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄

☄ Now, let's check whether the value of x is 3 or not!

<h3>☥ Verification :</h3>

\sf{15x - 7 = 2 + 12x}

\dashrightarrow{ \sf{15 \times 3 - 7 = 2 + 12 \times 3}}

\dashrightarrow{ \sf{45 - 7 = 2 + 36}}

\dashrightarrow{ \sf{38 = 38}}

L.H.S = R.H.S ( Hence , the value of x is 3 ).

✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄ ✄

<h3>✒ Rules for solving an equation :</h3>
  • If an equation contains fractions ,multiply each term by the L.C.M of denominators.
  • Remove the brackets , if any.
  • Collect the terms with the variable to the left hand side and constant terms to the right hand side by changing their sign ' + ' into ' - ' and ' - ' into ' + ' .
  • Simplify and get the single term on each side.
  • Divide each side by the coefficient of variable and then get the value of variable.

Hope I helped!

Have a wonderful time ! ツ

~TheAnimeGirl

5 0
2 years ago
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