Complete the expression 16𝑥 to the fourth blank plus 𝑦 squared to make a perfect square.
In order to make a perfect square, it is known that the middle term must be equal to plus or minus two times the square of the first term times the square of the third term. So we need to plug in the first term. And the first term is 16𝑥 to the fourth power.
And now for the third term, it is equal to 𝑦 squared. So we need to simplify. The square root of 16 is four, and the square root of 𝑥 to the fourth is 𝑥 squared. And now the square root of 𝑦 squared is 𝑦.
So now we simply need to multiply all of these together. Two times four is eight, and then 𝑥 squared and 𝑦 are just simply multiplied together. So we have plus or minus eight 𝑥 squared 𝑦. So this means, to complete our expression to make a perfect square, the middle term will need to be negative eight 𝑥 squared 𝑦 or positive eight 𝑥 squared 𝑦.