Answer:
B. (2x + 4y)(4x² - 8xy + 16y²)
Step-by-step explanation:
To factorize the polynomial 8x³ + 64y³, begin by expressing the numerical coefficients as cubes.
We can express 8 as 2³, and 64 as 4³, so:
[tex]8x^3 + 64y^3=2^3x^3 + 4^3y^3[/tex]
Apply the Product of Powers exponent rule: (aⁿbⁿ) = (ab)ⁿ.
[tex](2x)^3 + (4y)^3[/tex]
Now we can use the sum of cubes formula: a³ + b³ = (a + b)(a² - ab + b²).
[tex](2x + 4y)((2x)^2 - (2x)(4y) + (4y)^2)[/tex]
Simplify:
[tex](2x + 4y)(4x^2 - 8xy + 16y^2)[/tex]
Therefore, the correct factorization of the given polynomial is:
[tex]\Large\boxed{\boxed{(2x + 4y)(4x^2 - 8xy + 16y^2)}}[/tex]
