How would the sum of cubes formula be used to factor x3y3 + 343? Explain the process. Do not write the factorization.

2 answers:

4 0

The sum of cubes formula:
a³ + b³ = ( a + b ) ( a² - a b + b² )
x³ y³ = ( x y )³ and 343 = 7³
x³ y³ + 343 = ( x y )³ + 7³ = ( x y + 7 ) ( x² y² - 7 x y + 49 )

olga_2 [115]3 years ago

3 0

To factor, first identify the quantities that are being cubed. The first term is the cube of xy, and the constant is the cube of 7. Next, use the formula to write the factors. The first factor is the sum of xy and 7. The second factor has three terms: the square of xy, the negative of 7xy, and the square of 7.

You might be interested in

If two students from this college are selected at random, what is the probability that they are both males?

igor_vitrenko [27]

Answer:

$P(A_1 and A_2) = P(A_1) *P(A_2)= 0.3*0.3 =0.09$

Step-by-step explanation:

Assuming this problem :"Only 30% of the students in a certain liberal arts college are males. If two students from this college are selected at random, what is the probability that they are both males?"

Previous concepts

An independent event is an "event that has no connection to another event's chances of happening ". For this case we can assume that if one person is male and if we select another one the probability that this one would be male or female is totally indepedent from the first selection.

When we have two independent events let's say A and B and we want to find the probability that both events occurs at the same time we can use the following formula:

$P(A and B) = P(A)*P(B)$

Solution to the problem

We can define some notation:

$A_1$ first person selected is a male

$A_2$ second person selected is male

On this case we want the probability that both would be males. And we can express this like this on math terms:

$P(A_1 and A_2)$

For this case we can assume that the two events are independent. And in order to find the probability for two events independents events we just need to multiply the probabilities of each one like this:

$P(A_1 and A_2) = P(A_1) *P(A_2)= 0.3*0.3 =0.09$

5 0

3 years ago

It’s you birthday and you bought a giant sandwich to feed all of your guests. The sandwich is 10 1/2 feet long and you need to f

Hoochie [10]

Answer: $1\dfrac{3}{4}\text{ feet}$

Step-by-step explanation:

Given: Length of sandwich = $10\dfrac12\text{ feet}=\dfrac{21}{2}\text{ feet}$

Total people = 14

If everyone gets a same sized piece , then length of each piece should be

$\dfrac{\text{ Length of sandwich}}{\text{Total people}}$

$=\dfrac{\dfrac{21}{2}}{14}\text{ feet}\\\\=\dfrac{21}{2\times14}\text{ feet}\\\\=\dfrac{7}{2\times2}\text{ feet}\\\\=\dfrac{7}{4}\text{ feet}\\\\=1\dfrac{3}{4}\text{ feet}$