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
Andreas93 [3]
1 year ago
13

Factor completely x^8- 16.

Mathematics
2 answers:
Nataly_w [17]1 year ago
7 0

Answer:

Step-by-step explanation:


So in this example we'll be using the difference of squares which essentially states that: (a-b)(a+b)=a^2-b^2 or another way to think of it would be: a-b=(\sqrt{a}-\sqrt{b})(\sqrt{a}+\sqrt{b}). So in this example you'll notice both terms are perfect squares. in fact x^n is a perfect square as long as n is even. This is because if it's even it can be split into two groups evenly for example, in this case we have x^8. so the square root is x^4 because you can split this up into (x * x * x * x) * (x * x * x * x) = x^8. Two groups with equal value multiplying to get x^8, that's what the square root is. So using these we can rewrite the equation as:

x^8-16 = (x^4-4)(x^4+4)

Now in this case you'll notice the degree is still even (it's 4) and the 4 is also a perfect square, and it's a difference of squares in one of the factors, so it can further be rewritten:

x^4-4 = (x^2-2)(x^2+2)

So completely factored form is: (x^2-2)(x^2+4)(x^4+4)

I'm assuming that's considered completely factored but you can technically factor it further. While the identity difference of squares technically only applies to difference of squares, it can also be used on the sum of squares, but you need to use imaginary numbers. Because x^2+4 = x^2-(-4). and in this case a=x^2 and b=-4. So rewriting it as the difference of squares becomes: x^4+4 = x^4 - (-4) = (x^2-\sqrt{-4})(x^2+\sqrt{-4}) = (x^2-2i)(x^2+2i) just something that might be useful in some cases.

12345 [234]1 year ago
6 0

We can factor this into (x^{4}+4)(x^{4} -4).

This is because we use  difference of two squares where x^{2} -y^{2}  = (x+y)(x-y)

So we rewrite x^8-16 to x^8-4^2.

This can then be written to the equation I put at the start.

p.s. The reason its x^{4} is because x^{4} * x^{4}  = x^{8}
(P.S.S I just found that the other helper did it fully so I stopped here, read his, its correct)

You might be interested in
Priya has completed 9 exam questions. This is 60% of the questions on the exam. How many questions are on the exam?
USPshnik [31]

the whole exam will be 100%, and let's say that's "x" questions, but we also know that 9 is 60% of that so

\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} x&100\\ 9&60 \end{array}\implies \cfrac{x}{9}=\cfrac{100}{60}\implies \cfrac{x}{9}=\cfrac{5}{3}\implies 3x=45 \\\\\\ x=\cfrac{45}{3}\implies x=15

8 0
2 years ago
Find x pls help me this is due soon
seraphim [82]

Answer:

x=35

hope it helps..........

8 0
3 years ago
Help please I’m really struggling
WITCHER [35]

Answer:

It’s d

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
The L.L. Bean men’s cotton chambray shirt comes in the following colors: blue, stone, rust, green, plum, and indigo. In addition
bulgar [2K]

Answer:

<u>60 types of cotton chambray shirts can be produced</u>

<u />

Step-by-step explanation:

The shirt comes in the following colors: blue, stone, rust, green, plum, and indigo

<u>Number of colors the shirt comes in = 6</u>

The shirt comes in the following sizes: small (S), medium (M), large (L), extra large (XL), and extra extra large (XXL)

<u>Number of sizes the shirt comes in = 5</u>

The shirt comes in the following styles: short sleeves or long sleeves

<u>Number of styles the shirt comes in = 2</u>

<u />

Total number of cotton chambray shirts that can be produced are:

No. of colors * No. of sizes * No. of styles

6 * 5 * 2

60 shirts

<u>So, </u><u>60 types of cotton chambray shirts can be produced</u><u> from the given options of colors, sizes and styles. </u>

7 0
3 years ago
PLZ HELP DONT UNDERSTAND!!!
victus00 [196]
\bf \textit{area of a triangle}=A=\cfrac{1}{2}bh\qquad &#10;\begin{cases}&#10;b=base\\&#10;h=\textit{height or altitude}&#10;\end{cases}\\\\&#10;-----------------------------\\\\&#10;\textit{area of a trapezoid}\\\\&#10;A=\cfrac{h}{2}(a+b)\qquad &#10;\begin{cases}&#10;a=\textit{base, or one of the parallel sides}\\&#10;b=\textit{base, or the other parallel side}\\&#10;h=\textit{height, the distance between both}\\&#10;\qquad \textit{parallel sides}&#10;\end{cases}
7 0
3 years ago
Other questions:
  • It should take 5.22 minutes to clean a shower. You have 5 showers that need to be cleaned. How many minutes should it take for y
    15·1 answer
  • What are the coordinates of the vertex of the graph of f(x)=2|x−3| ? Enter your answer in the boxes.
    9·2 answers
  • The triangle ABC in the figure provided has midpoints labeled M and N and O.
    9·2 answers
  • Send help please I am confused aaa According to the distributive law, what operation goes in the blank? -(8 - 7) = - 8 __ 7
    14·1 answer
  • If the area of a park is exactly halfway between 2.4 and 2.5 acres, what I think area of the park
    14·2 answers
  • En una radio, 1/8 del dia esta destinado a emitir publicidad. Del total de publucidad, 3/5 corresponden a comerciales de univerc
    6·1 answer
  • What equivalent to 3:4<br> Please no bots
    11·2 answers
  • HELP ILL GIVE BRAINLIEST
    15·1 answer
  • A $900 notebook computer is discounted 5%. What is the sale price of the computer?
    7·1 answer
  • Please help Find P2 if possible.
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!