Question

Select the correct product. (x^2+4)(x^2-4)​

1. X^4-16
2. X^4+16
3. X^2+8x+16
4. X^2-8x-16

Answer 1

The correct answer is 1. x^4 - 16.
It is simply a hard version of the difference between two squares

Answer 2

`({x}^(2) + 4 )( {x}^(2) - 4) \\ 1)( {x}^(2) - 16) \\ = (x - 4)(x + 4) \\ 2)( {x}^(2) + 16) \\ = (x - 4)(x + 4) \\ 3) {x}^(2) + 8x + 16 \\ {x}^(2) + (4 + 4)x + 16 \\ {x}^(2) + 4x + 4x + 16 \\ x(x + 4) + 4(x + 4) \\ (x + 4)(x + 4) \\ 4) {x}^(2) - 8x - 16 \\ {x}^(2) - (4 + 4)x - 16 \\ {x}^(2) - 4x + 4x - 16 \\ x(x - 4) + 4(x - 4) \\ (x - 4)(x + 4)`