Question

what is the factored form of 343 + x⁶?
a. (7 - x)(49 + 7x + x²)
b. (7 + x)(49 - 7x + x²)
c. (7 - x²)(49 + 7x² + x⁴)
d. (7 + x²)(49 - 7x² + x⁴)

Explanation:

We use the sum of cubes formula: \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). Here, \(343 = 7^3\) and \(x^6=(x^2)^3\), so \(a = 7\), \(b=x^2\). Substituting into the formula gives \((7 + x^2)(49 - 7x^2+x^4)\), which matches option D.

Answer:

\(\boxed{D}\)