All categories

3 years ago

Factor the expression: x^6-729. Show your work Please.

Mathematics

1 answer:

Brut [27]3 years ago

7 0

Answer:

(x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)

Step-by-step explanation:

Use of formulas:

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

Given the expression:

x^6-729

Factoring 729

729 = 3*3*3*3*3*3 = 3^6

Factoring the expression

x^6 - 3^6 =
(x^3)^2 - (3^3)^2 =
(x^3 + 3^3)(x^3 - 3^3) =
(x + 3)(x^2 -3x + 9)(x - 3)(x^2 + 3x + 9) =
(x + 3)(x - 3)(x^2 -3x + 9)(x^2 + 3x + 9)

You might be interested in

Which is bigger? 2^4 or 4^2?

vovikov84 [41]

Answer:

Both are equal

Step-by-step explanation:

$2^4 = 16 \\ \\ {4}^{2} = 16 \\ \\ \implies \: {2}^{4} = {4}^{2}$

8 0

2 years ago

Read 2 more answers

If a simple harmonic motion is described by x = 3 cos(πt), starting from t = 0 s, what is the first occurrence of a value of t f

poizon [28]

Answer:

The first occurence of t for which x = 0 is t = 0.5.

Step-by-step explanation:

The harmonic motion is described by the following equation.

$x(t) = 3\cos{\pi t}$

What is the first occurrence of a value of t for which x = 0?

This is t when $x(t) = 0$ . So

$x(t) = 3\cos{\pi t}$

$3\cos{\pi t} = 0$

$\cos{\pi t} = \frac{0}{3}$

$\cos{\pi t} = 0$

The inverse of the cosine is the arcosine. So we apply the arcosine function to both sides of the equality.

$\arccos{\cos{\pi t}} = \arccos{0}$

$\pi t = \frac{\pi}{2}$

$t = \frac{\pi}{2 \pi}$

$t = \frac{1}{2}$

$t = 0.5$

The first occurence of t for which x = 0 is t = 0.5.

3 0

2 years ago

How do I find the equation for the line?

GrogVix [38]

Answer:

The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept.

7 0

2 years ago

I need help ASAP The angle measures of a triangle are shown in the diagram. 50° les (3x - 10) ° What is the value of x? F25 G 20

insens350 [35]

Answer:

The answer is 28

Step-by-step explanation:

Since the total measurements of triangle corners are equal to 180

Then

$2x + 3x - 10 + 50 = 180 \\ 5x - 40 = 180 \\ 5x = 140 \\ x = 28$

4 0

2 years ago

Find the value of x

riadik2000 [5.3K]

Answer:

4√5

Step-by-step explanation:

Use Pythagorean theorem

a^2=21^2-19^2

a^2=441-19^2

a^2=441-361

a^2=80

a= √80

simplify

6 0

2 years ago