Factorise.. y^4 +1/y^4 +1
If you meant:
(y^4 +1)/(y^4 +1)
then
= 1
end of story
Hey, didn't I do this one for you earlier this morning ????
Why are your reposting it again??
https://www.jiskha.com/questions/1827397/a-4-4-4-a-4-1factorise-1-is-not-included-4a-4
don't forget that
y^4 + 1 = y^4 + 2y^2 + 1 - 2y^2
= (y^2+1)^2 - 2y^2
= (y^2+1 + √2 y)(y^2+1 - √2 y)
Though not really relevant here since, as Reiny pointed out, the result is just 1
Which is the answer I had given Shehzad in the earlier post
https://www.jiskha.com/questions/1827397/a-4-4-4-a-4-1factorise-1-is-not-included-4a-4
Don't know why he/she had to repost it.
To factorize the expression y^4 + 1/y^4 + 1, we need to recognize a pattern. Let's break it down step by step:
We can rewrite the expression as follows:
y^4 + 1/y^4 + 1 = (y^4 * y^4 + 1 + y^4) / y^4
Now, we notice that the numerator has a perfect square in it: y^4 * y^4 = (y^2)^4
So, we can rewrite the expression as:
[((y^2)^4 + 1) + y^4] / y^4
Now, we have a sum within parentheses. The sum (a^2 + 1) cannot be further simplified or factored.
So, the final factorization of the expression is:
[((y^2)^4 + 1) + y^4] / y^4
Note: In some cases, expressions cannot be factored further. It's important to recognize patterns and common factorization methods to simplify and factorize expressions.