Question

Which of the following should be added to make x power 4 +64 a perfect square​

Answer 1

Answer:

16x²

Step-by-step explanation:

since

A²+B²+2AB = (A+B}²

=> (x²)²+(8)² +2x²×8 is a perfect square

=> 16x² should be added to make perfect square of the given polynomial .

Hope this helps you

Answer 2

Answer:

The Correct Answer would be 16x² or 2×x²×8. The terms that should be added to x⁴ + 64 to make it a perfect square is 16x² or 2×x²×8.

Step-by-step explanation:

Given: The number we have to make a perfect square. It being = x⁴ + 64.

To Find: The number that should be added to it to make it a perfect square.

Now, the given equation = x⁴ + 64.

For making it a perfect square by adding a term, we first have to compare the equation with the standard equation of square of adding two numbers, which is =

                              ( a + b )² = a² + b² + 2ab

On comparing, we can see:

a² = x⁴  ⇒   a = x²

b² = 64  ⇒  b = 8

Hence, we have to find 2×a×b.

We know a as well as b. Therefore, we can easily find 2ab.

2ab = 2×8×x²

       = 16x²

Hence, 16x² the correct answer, giving the formula as:

                          ( x² + 8 )² = (x²)² + 8² + 16x²