Answers
Answer: The equation is not an identity
==========================================================
Explanation:
We'll expand out the right hand side to see if we can simplify it to the left hand side. The stuff on the left will stay the same for each step.
I'll use c = a+b as a way to help distribute.
[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = c(a^3 - a^2b-ab^2 + b^3)\\\\a^4 + b^4 = a^3c - a^2bc-ab^2c + b^3c\\\\a^4 + b^4 = a^3(c) - a^2b(c)-ab^2(c) + b^3(c)\\\\a^4 + b^4 = a^3(a+b) - a^2b(a+b)-ab^2(a+b) + b^3(a+b)\\\\a^4 + b^4 = a^4+a^3b - a^3b-a^2b^2-a^2b^2-ab^3 + ab^3+b^4\\\\a^4 + b^4 = a^4+(a^3b - a^3b)+(-a^2b^2-a^2b^2)+(-ab^3 + ab^3)+b^4\\\\a^4 + b^4 = a^4-2a^2b^2+b^4\\\\[/tex]
Unfortunately, we can't go any further. We have a^4 and b^4 on the right hand side, but we also have the term -2a^2b^2 that didn't cancel out. Therefore, the original equation is not an identity.
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Here's another way you can see that we don't have an identity.
Let's say we fixed 'a' to be equal to 1.
That means the equation
[tex]a^4 + b^4 = (a+b)(a^3 - a^2b-ab^2 + b^3)[/tex]
would turn into
[tex]1^4 + b^4 = (1+b)(1^3 - 1^2b-1b^2 + b^3)[/tex]
and simplify to
[tex]1 + b^4 = (1+b)(1 - b-b^2 + b^3)[/tex]
Now replace b with x and you'll have the two equations to represent the left and right hand sides
[tex]y = 1+x^4\\y = (1+x)(1-x-x^2+x^3)[/tex]
which you can graph on the same xy axis. You should note that the two equations produce different curves. The curves would need to be identical if we wanted an identity to happen.
Side note: you can pick other values for 'a' instead of just 1.
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Step-by-step explanation:
What is the value of the expression
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Answers
Answer:
[tex]3 - 4 = 1[/tex]
✨✨
3-4
you just need to subtract 3 from -4
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[tex]6x -2\frac{1}{2}[/tex]
Step-by-step explanation:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Simplify. √25a^2.
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Answers
The square root of 25 is 5 and the square root of a^2 is a.
Hope this helps and if possible could I please have the brainliest answer?
A bird flies down from a higher elevation to a lower elevation at a rate of 3 meters per second. Which equation models the bird's change in elevation, in meters, after 120 seconds?
O A. (-120)(-3) = -360
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Answers
Answer:
D
Step-by-step explanation:
Answer: The answer is 120(-3)= -360
Step-by-step explanation:
A. P. E. X.
Tell whether the ordered pair is a solution to the equation.
(4, 4); y = -x + 8
Answers
Answer:
Yes, it is.
Step-by-step explanation:
(4) = -(4)+8
4=4
True
a local company uses 13 1/2 tons of paper in one week. It recycles about 1/3 of its waste. how many tons of paper does the company recycle in one week?
Answers
Answer:
4 1/2 tons of recycled paper
Step-by-step explanation:
13.5/3 = 4.5 or 4 1/2
Terre Haute to Indianapolis to Bloomington measure 3 cm on the map. What is the actual distance?
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b) 150 km
c) 200 km
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Answers
From the information given, it can be deduced that the actual distance from Terre Haute to Indianapolis to Bloomington is 150km.
From the complete information, we are told that on the map of Indiana, 1cm = 50km.
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Answer:
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Step-by-step explanation:
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2. A. 300 km
3. D. 7.5 cm
4. B. 30 yd ^ 2
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i hope this helps please coment if you can! = ) <3
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Answer:
Step-by-step explanation:
Answer:
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Step-by-step explanation:
y=(x-1)²-3
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Answers
Answer:
the answer : a
equation : 35 = x
35 = 7
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Hey there!
(35 ÷ x) - 2
= (35 ÷ 7) - 2
= (5) - 2
= 5 - 2
= 3
Therefore, your answer is: Option A. 3
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
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Answers
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Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answer:
x = 250 minutes
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
If a coordinate point is at (4, 2) and is translated down 3 units and right 1 unit, what is its new coordinate point?
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Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
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Answers
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Answer:
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Step-by-step explanation:
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Answers
Answer:
A
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Answers
Answer:
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Answers
Answer:
3.416 x 10^(" + * + 1)
Step-by-step explanation:
The exponents of (5.6 x 10") (6.1 x 10* ) seem incorrect. Whatever they are, do the following:
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Answers
Step-by-step explanation:
There are 17 hours between 7:45 to 1:00
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Answers
Answer:
400 [tex]ft^{2}[/tex] (Don't forget the square symbol!)
Step-by-step explanation:
For the triangle:
Base times height divided by 2.
8 x 25 = 200
200/2 = 100
For the regtangle:
Width times height.
25 x 12 = 300
Add them together, and you get:
100 + 300 = 400.
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Step-by-step explanation:25*12=300
25
x12
50
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Answers
Answer:
16 m
Step-by-step explanation:
12² + b² = 20²
I hope this helps!
Answer:
b = 16 m
Step-by-step explanation:
Using Pythagoras' identity in the right triangle
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
b² + 12² = 20²
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Max can run 10 miles in 2 hours. At this rate, how long will it take him to run 25 miles
Answers
Answer:
Step-by-step explanation: 10 miles per 2 hours is the First step. Knowing this helps a lot. Next you need to understand your solving for 25 miles. 10 goes into 25 2.5 times. This means you need to multiply the time by 2.5 as well. That would be 5 hours.
Hassan picked 5 pounds of strawberries. That afternoon, Hassan's sister ate 1/4 of the strawberries. How many pounds of strawberries did Hassan's sister eat? Write your answer as a fraction or as a whole or mixed number.PLZZZZZZZ HELP
Answers
Answer:
Hassan's sister ate 5/4 pounds of strawberries.
Step-by-step explanation:
=> 5 x 1/4=> 5/4Conclusion:
Therefore, Hassan's sister ate 5/4 pounds of strawberries.
Hoped this helped
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