Answer: ** First answer ---> the number to add on the end is 169
** Second answer ---> (y - 13)²
Explanation:
If I understand correctly, you want to add something to y² -26y that will turn the expression into a trinomial (3 term expression) that can be factored into a binomial, squared.
Take the coefficient of the second term, the one that has y to the first power, and divide that coefficient by 2.
Then square the result.
-26/2 = -13
(-13)² = 13² = 169
** First answer ---> the number to add on the end is 169
Now add that square onto the end of the original expression.
y² -26y +169
Now factor that:
(y - 13)² = (y - 13)(y - 13) = y² - 26y + 169 (by using FOIL)
** Second answer ---> (y - 13)²
NOTE: If the expression y² -26y was part of an equation, we could not just add 169 for our convenience. That would throw one side of the equation out of balance!
We would have to either add 169 to the other side of the equation as well, or else subtract 169 someplace in the same side where we added 169.
I hope this all helps!