hi. - I am not sure how to do this.-
You have to factor completley.
5y^8-125
Hi! I'd be happy to help you factor the expression 5y^8 - 125.
To factor the expression completely, we'll follow a process called factoring by the difference of squares. The difference of squares formula states that a^2 - b^2 can be factored as (a + b)(a - b).
Now let's apply this formula to our expression:
5y^8 - 125
First, we notice that 125 is a perfect cube, which means it can be written as 5^3. So, we can rewrite the expression as:
5y^8 - 5^3
Now, we have a common factor of 5, which we can factor out:
5(y^8 - 5^3)
Next, we can observe that y^8 is a perfect square, which means it can be written as (y^4)^2:
5((y^4)^2 - 5^3)
Using the difference of squares formula, we factor the expression inside the brackets:
5(y^4 + 5)(y^4 - 5^3)
And that's the factored form of the expression 5y^8 - 125! It can be written as 5(y^4 + 5)(y^4 - 125).