All categories

3 years ago

What is the factored form x^3 - 1 ?

Mathematics

1 answer:

amid [387]3 years ago

7 0

Answer: x^3 - 1 = (x - 1)(x^2 + x + 1)

Explanation:

This is a type of factorizing called the sum or difference of 2 cubes:

a^3 - b^3 = (a - b)(a^2 + ab + b^2)

The sum of the cubes is factored as:

a^3 + b^3 = (a + b)(a^2 - ab + b^2)

In this case, we have: x^3 - 1 so follow the rule above.

x^3 - 1 = (x - 1)(x^2 + x + 1)

You might be interested in

Calculate the volume of blood moved per minute by a heart at rest.A heart "at rest" beats at a rate of 72 beats per minute and m

Travka [436]

Answer:

70 X 72 = 5040 mL per minute

6 0

3 years ago

Which expression is equivalent to (16 x Superscript 8 Baseline y Superscript negative 12 Baseline) Superscript one-half?.

loris [4]

To solve the problem we must know the Basic Rules of Exponentiation.

<h2>Basic Rules of Exponentiation</h2>

$x^ax^b = x^{(a+b)}$
$\dfrac{x^a}{x^b} = x^{(a-b)}$
$(a^a)^b =x^{(a\times b)}$
$(xy)^a = x^ay^a$

$x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4$

The solution of the expression is $\dfrac{4x^4}{y^6}$ .

<h2>Explanation</h2>

Given to us

$(16x^8y^{12})^{\frac{1}{2}}$

Solution

We know that 16 can be reduced to $2^4$ ,

$=(2^4x^8y^{12})^{\frac{1}{2}}$

Using identity $(xy)^a = x^ay^a$ ,

$=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}$

Using identity $(a^a)^b =x^{(a\times b)}$ ,

$=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})$

Solving further

$=2^2x^4y^{-6}$

Using identity $\dfrac{x^a}{x^b} = x^{(a-b)}$ ,

$=\dfrac{2^2x^4}{y^6}$

$=\dfrac{4x^4}{y^6}$

Hence, the solution of the expression is $\dfrac{4x^4}{y^6}$ .

Learn more about Exponentiation:

brainly.com/question/2193820

8 0

2 years ago

Please I need help I can’t get a bad grade I try my best but I don’t understand

olya-2409 [2.1K]

Answer: What do you need, what grade are you in?

Step-by-step explanation:

3 0

3 years ago

Is -20 an irrational number or rational number

Gekata [30.6K]

Answer: Rational number

Step-by-step explanation:

Let's write out the properties of rational and irrational numbers.

Rational

Integers
Whole numbers
finite decimals
repeating decimals

Irrational

not rational numbers

------------------------------------------------------------------------------------------------------------

Looking at the list we made, we can say that -20 is a rational number. -20 is an integer and a whole number. Therefore, it is a rational number.

3 0

3 years ago

Read 2 more answers

If the population of a country grows at a rate of approximately 5 percent per year, the number of years required for the populat

iogann1982 [59]

THe number of years would be 20 years.

8 0

3 years ago