Solve y=x^2-5 for x

What is the coeffieent of (x^4)(y^4) in the expansion of (x+y)^8

kap26 [50]

ANSWER

The coefficient is 70.

EXPLANATION

The given binomial expression is

$(x+y)^8$

The specific term of a binomial expansion can be determined using the formula,

$T_{r+1}= nC_ra^{n-r}b^r$
where

$n=8,r=4,a=x,b=y$

We substitute these values into the formula to get,

$T_{4+1}= 8C_4x^{8-4}y^4$

We simplify to get,

$T_{5}= 70x^{4}y^4$

Hence the coefficient is 70.

4 0

3 years ago

Directions : Factor each of the following Differences of two squares and write your answer together with solution

N76 [4]

$\huge \boxed{\mathfrak{Question} \downarrow}$

Factor each of the following differences of two squares and write your answer together with solution.

$\large \boxed{\mathbb{ANSWER\: WITH\: EXPLANATION} \downarrow}$

$\sf \: x ^ { 2 } - 36$

Rewrite $\sf\:x^{2}-36 as x^{2}-6^{2}$ . The difference of squares can be factored using the rule: $\sf\: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(x-6\right)\left(x+6\right) }}$

__________________

$\sf \: 49 - x ^ { 2 }$

Rewrite 49-x² as 7²-x². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf \: \left(7-x\right)\left(7+x\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-x+7\right)\left(x+7\right) }}$

__________________

$\sf \: 81 - c ^ { 2 }$

Rewrite 81-c²as 9²-c². The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\sf\left(9-c\right)\left(9+c\right)$

Reorder the terms.

$\boxed{ \boxed{ \bf\left(-c+9\right)\left(c+9\right) }}$

__________________

$\sf \: m ^ { 2 } n ^ { 2 } - 1$

Rewrite m²n² - 1 as $\sf\left(mn\right)^{2}-1^{2}$ . The difference of squares can be factored using the rule: $\sf\:a^{2}-b^{2}=\left(a-b\right)\left(a+b\right)$ .

$\boxed{ \boxed{ \bf\left(mn-1\right)\left(mn+1\right) }}$

4 0

3 years ago

Read 2 more answers

A padlock has a four-digit code that includes digits from 0 to 9, inclusive. What is the probability that the code does not cons

Eduardwww [97]

Since there is no repetition allowed, there are 10 possibilities for the 1st digit, 9 for the 2nd, 8 for the 3rd, and 7 for the 4th. This gives a total of (10)(9)(8)(7) = 5040 four-digit codes.
For all odd digits to be used, there are 5 possibilities for the 1st digit (1,3,5,7,9), 4 for the 2nd, 3 for the 3rd, 2 for the 4th. This gives a total of (5)(4)(3)(2) = 120 codes that only use odd digits.
Therefore there are 5040 - 120 = 4920 codes that do not consist of all odd digits. The probability is 4920/5040 = 41/42.

4 0

3 years ago

Read 2 more answers

Melanie made 72 peanut butter cookies and oatmeal cookies. She wants to make identical groups of cookies for her friends. Each g

swat32

This depends on how many friends she has. Like if she has 72 friends each will get one of each, but if she has 3 friends than each will get 24 on each. Do you know how many friends she has?

7 0

3 years ago

How many times can 1021 go into 6

mina [271]

Answer:

uh i really wanna help but maybe dividing would help :)

Step-by-step explanation:

8 0

2 years ago

Solve y=x^2-5 for x​

Solve y=x^2-5 for x