Answer :
Final answer:
The expression 125x^6 + y^6 can be factorised using the sum of two cubes formula to give (5x^2 + y^2)(25x^4 - 5x^2y^2 + y^4), which corresponds to option A.
Explanation:
The expression 125x^6 + y^6 can be factorised using the formula for the sum of two cubes, which states that a^3 + b^3 = (a + b)(a^2 - ab + b^2).
Here, you need to recognize that 125x^6 is (5x^2)^3 and y^6 is (y^2)^3.
You are then looking for the sum of two cubes.
So following the formula, the factorised expression will be (5x^2 + y^2)((5x^2)^2 - 5x^2*y^2 + (y^2)^2) which simplifies to (5x^2 + y^2)(25x^4 - 5x^2y^2 + y^4). Therefore, the correct answer is option (A).
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