Which of the following below shows the expression below in simplest form?
2y^2 - 50/y - 5 Is it "C"
A. 2(y-5)
B. 2(x +50)
C. 2(y+5)
D. 2(y^2 +5)
that is correct
but online, use parens:
(2y^2 - 50)/(y - 5)
Thanks, Steve. You are always so helpful.
To simplify the expression 2y^2 - 50/y - 5, we need to find the common factors in each term and then combine like terms.
First, let's identify any common factors in each term:
In the term 2y^2, the only common factor is 2.
In the term -50/y, there is a common factor of 10 which we can factor out of the numerator.
Therefore, the expression can be rewritten as:
2 * (y^2 - 25/y) - 5
Now, let's simplify further.
In the parentheses, we can see that we have a difference of squares:
y^2 - 25 = (y + 5)(y - 5)
So the expression becomes:
2 * (y + 5)(y - 5)/y - 5
There is no need to factor out any common factors further, so this is the simplest form of the expression.
Now let's check which of the options matches the simplest form:
A. 2(y-5)
B. 2(x + 50) <-- This option does not match the original expression.
C. 2(y+5) <-- This option matches the simplified form.
D. 2(y^2 + 5) <-- This option does not match the simplified form.
Therefore, the correct answer is option C. 2(y+5).