16y^{2}-40y+?
I really need to figure out what the question mark is, but I am so confused.
You are probably studying completing the square.
Study the result of something like
(5x-6)^2
the result is 25x^2 - 60x + 36
notice if you take the square roots of the first and last numbers, multiply them and double you get the middle number.
now reverse that thinking for your given case
16y^2 - 40y + ????
Did you get 25?
To find the value of the question mark, you need to complete the square in order to factor the expression.
Start by looking at the coefficient of the y^2 term, which is 16. Take half of that coefficient and square it: (16/2)^2 = 8^2 = 64.
Now, rewrite the expression by adding and subtracting this value inside the parentheses:
16y^2 - 40y + 64 - 64.
The first three terms inside the parentheses can be factored as a perfect square: (4y - 4)^2 = 16y^2 - 32y + 16.
Now, rewrite the expression again, combining like terms:
(16y^2 - 32y + 16) - 64.
Simplify further:
16y^2 - 32y + 16 - 64 = 16y^2 - 32y - 48.
So, the value of the question mark is -48.