Question

Factors of x⁴ + 4y⁴ are ______.

Options

• (x² + 2xy + 2y²) (x² – 2xy + 2y²)

• (x² + 2y²) (x² + 2y²)

• (x² – 2y²) (x² – 2y²)

• None of these

Answer 1

Factors of x⁴ + 4y⁴ are (x² + 2xy + 2y²) (x² – 2xy + 2y²).

Explanation:

This expression can be factored using the Sophie Germain identity, which states that for expressions of the form (a⁴ + 4b⁴), the factorization is:

a⁴ + 4b⁴ = (a² + 2ab + 2b²)(a² – 2ab + 2b²)

Applying this for (a = x) and (b = y), we get the factors as above.

Therefore. (x² + 2xy + 2y²) (x² – 2xy + 2y²).