Which of the following is equivalent to the expression above?

The correct answer is:

Hint: 
The concept used in this question is of algebraic expressions or expressions.
The algebraic expression is any mathematical statement. It is consists of numbers, variables and an arithmetic operation between them.
Expressions do not have fixed value.
Try to simplify the expression by factorising.
Step by step explanation:
Given:
Expression: x⁴ − 8x² + 16
Step 1:
So, the equation will can be written as,
⇒ (x²)²  − 8(x²) + 16
Let x² be y
The equation will become
⇒ (y)²  − 8(y) + 16
⇒ y² − 8y + 16
Step 2:
Factorize the above equation.
⇒ y² − 8y + 16 {General form is ax² + bx + c}
Now multiply a and c,
If sign of ac is +ve, split b as sum of factors of ac,
If sign of ab is -ve, split b as subtraction of factors of ac,
In above expression,

And sign of ac is +ve
∴ b = - 4 + (- 4) as factors of 16 = 1  16
- 8 = - 4 + (- 4) = 2 × 8
= 4 × 4
⇒ y² − 4y - 4y + 16
⇒ (y² − 4y) - (4y + 16)
⇒ y(y − 4) - 4(y - 4)
⇒ (y − 4) (y - 4)
⇒ (y − 4)²
Step 3:
Put x² in place of y, we will get
⇒ (x² − 4) (x² − 4))
This can be written as,
⇒ [(x)² − (2)²] [(x)² − (2)²]
Step 4:
Use the identity.
(a² - b²) = (a + b) (a - b)
∴ [(x)² − (2)²] [(x)² − (2)²]
⇒ [(x + 2) (x - 2)] [(x + 2) (x - 2)]
⇒ (x + 2)² (x - 2)²
Hence, the answer is (x + 2)² (x - 2)².