Factorise 25k^2-20+(4/k^2)
I suspect a perfect square, since I noticed that the first and last terms are perfect squares, so my suspicion points to
(5k ..... 2/k)^2
the middle term is negative, so I guess at
(5k - 2/k)^2
check:
(5k - 2/k)(5k - 2/k)
= 25k^2 -10k/k - 10k/k + 4/k^2
= 25k^2 - 20 + 4/k^2 , I was right.
To factorize the expression 25k^2 - 20 + (4/k^2), we need to look for terms that have common factors. Let's break it down step by step:
Step 1: Look for common factors within the first two terms.
The first two terms, 25k^2 - 20, do not have any common factors other than 1.
Step 2: Look for common factors between the first two terms and the last term.
We need to find a common factor between 25k^2 - 20 and 4/k^2. To do this, we can multiply the second term, 4/k^2, by k^2 to make the denominator of the fraction match the denominator of the first two terms:
(4/k^2) * (k^2) = 4
Now we can rewrite the expression as:
25k^2 - 20 + 4
Step 3: Combine the simplified terms.
Now that we have removed the fraction and simplified the expression, we can combine like terms:
25k^2 - 20 + 4 = 25k^2 - 16
So, the factorized form of 25k^2 - 20 + (4/k^2) is 25k^2 - 16.