Question

Find the value of \( (2^{1/4} - 1) (2^{3/4} + 2^{1/2} + 2^{1/4} + 1) \)

• A. \( 1 \)
• B. \( 2 \)
• C. \( 0 \)
• D. \( 12 \)
• E.

Hint:

When dealing with powers of 2, approximate the values for easier multiplication, especially when the values are close to an integer.

Answer 1

The Correct Option is A

Step 1: Let \( x = 2^{1/4} \). This means that: \[ x^4 = 2 \] Thus, we can rewrite the expression as: \[ (x - 1) \left( x^3 + x^2 + x + 1 \right) \] Step 2: Observe that the expression \( (x - 1) \left( x^3 + x^2 + x + 1 \right) \) is a factorization of the difference of cubes: \[ (x - 1) \left( x^3 + x^2 + x + 1 \right) = x^4 - 1 \] Step 3: Substituting \( x^4 = 2 \) into the equation: \[ x^4 - 1 = 2 - 1 = 1 \] Thus, the value of the expression is \( 1 \).