Which of the following is the correct factorization of the polynomial below?27x3 + 64y3A.(4x + 3y)(2x +8y)B.(4x + 3y)(9x2 - 12xy + 16y2)C.(3x + 4y)(9x2 - 12xy + 16y2)D.The polynomial is irreducible.
Question
Which of the following is the correct factorization of the polynomial below?27x3 + 64y3A.(4x + 3y)(2x +8y)B.(4x + 3y)(9x2 - 12xy + 16y2)C.(3x + 4y)(9x2 - 12xy + 16y2)D.The polynomial is irreducible.
Solution
The given polynomial is a sum of cubes. The sum of cubes formula is a^3 + b^3 = (a + b)(a^2 - ab + b^2).
Here, a = 3x and b = 4y.
So, the correct factorization of the polynomial 27x^3 + 64y^3 is (3x + 4y)(9x^2 - 12xy + 16y^2).
Therefore, the correct answer is C. (3x + 4y)(9x^2 - 12xy + 16y^2).
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