1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Zinaida [17]
3 years ago
9

Factor completely.

c{1}{81}" alt="x^{8}-\frac{1}{81}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Eduardwww [97]3 years ago
6 0

We have 3⁴ = 81, so we can factorize this as a difference of squares twice:

x^8 - \dfrac1{81} = \left(x^2\right)^4 - \left(\dfrac13\right)^4 \\\\ x^8 - \dfrac1{81} = \left(\left(x^2\right)^2 - \left(\dfrac13\right)^2\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(\left(x^2\right)^2 + \left(\dfrac13\right)^2\right) \\\\ x^8 - \dfrac1{81} = \left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)

Depending on the precise definition of "completely" in this context, you can go a bit further and factorize x^2-\frac13 as yet another difference of squares:

x^2 - \dfrac13 = x^2 - \left(\dfrac1{\sqrt3}\right)^2 = \left(x-\dfrac1{\sqrt3}\right)\left(x+\dfrac1{\sqrt3}\right)

And if you're working over the field of complex numbers, you can go even further. For instance,

x^4 + \dfrac19 = \left(x^2\right)^2 - \left(i\dfrac13\right)^2 = \left(x^2 - i\dfrac13\right) \left(x^2 + i\dfrac13\right)

But I think you'd be fine stopping at the first result,

x^8 - \dfrac1{81} = \boxed{\left(x^2 - \dfrac13\right) \left(x^2 + \dfrac13\right) \left(x^4 + \dfrac19\right)}

You might be interested in
In a survey of 500 people, 31% said they were afraid of flying. What decimal represents the number of people who said they were
Elden [556K]

Answer:

.31

Step-by-step explanation:

155 / 5        31/100

500/ 5

31÷100

Long Division for 31 divided by 100

round to a Max of 3 Decimal gives us

=0.31

6 0
3 years ago
2x(squared) + 23x-19=0
Helen [10]
Use quadratic formula

for ax^2+bx+c=0
x=\frac{-b+/- \sqrt{b^2-4ac} }{2a}

given
2x^2+23x-19=0
a=2
b=23
c=-19

x=\frac{-23+/- \sqrt{23^2-4(2)(-19)} }{2(2)}
x=\frac{-23+/- \sqrt{529-152} }{4}
x=\frac{-23+/- \sqrt{377} }{4}

x=\frac{-23+ \sqrt{377} }{4} or \frac{-23- \sqrt{377} }{4}
7 0
3 years ago
5) Solve 5 - 2x &lt; 7.<br> A) x &lt; -1<br> B) x&gt;-1<br> 0x&lt;-12<br> D) X &gt; -12
Bingel [31]

Answer:

i think B. x>-1 is answer

Step-by-step explanation:

good luck

6 0
2 years ago
Rickey has fraction 7/8 of a cup of cereal in a bowl. He then gave two fraction 1/4 cups of cereal from his bowl to his little s
Zinaida [17]
5/8 would be the answer..

<span><span>7/8</span>-<span>1/4</span></span><span>=<span>(7 × 4) - (1 × 8)8 × 4</span></span><span>=<span>20/ 32</span></span><span>=<span>20 ÷ 432 ÷ 4</span></span><span>=<span>5/8<span>

</span></span></span>

4 0
3 years ago
Read 2 more answers
X≤−2 and x&lt;−5 on a number line
sweet [91]

x is less than or equal to -2.

x is greater than -5.

When x is less than something, the arrow must go left. <———

When x is equal to a number, the dot must be filled in.    •

When x is greater than a number, the arrow should go right, toward the greater values. ——>

When x isn’t equal to the number, the circle is not colored in. ⭕️

Shown in picture:

4 0
3 years ago
Other questions:
  • What is the square root of 69
    14·1 answer
  • What is the mean for the following set of data?
    10·2 answers
  • What info is required
    7·1 answer
  • What is the length of Line segment S R?
    10·1 answer
  • What is the slope of the line ?
    14·1 answer
  • Which linear inequality is represented by the graph?
    6·2 answers
  • Danyel took a test that had 20 questions on it. He got 4/5 of the question correct. How many questions did he get correct?
    6·1 answer
  • Find the length of side AB.
    5·1 answer
  • R+sy=t solving for y
    11·1 answer
  • The product is???<br><br> It is multiplication.
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!