125c^3 + 729x^3
(5c)^3 + (9x)^3
(5c + 9x)(25c^2 - 45cx + 81x^2)
Is this correct?
Yes.
Thanks
Yes. Note that the second term in parentheses cannot also be factored without using imaginary numbers
Yes, that is correct. The expression can be simplified using the formula for the sum of cubes, which states that \(a^3 + b^3\) can be factored as \((a + b)(a^2 - ab + b^2)\).
In this case, we have \(125c^3 + 729x^3\), which can be written as \((5c)^3 + (9x)^3\).
Using the formula for the sum of cubes, we can factor it as \((5c + 9x)((5c)^2 - (5c)(9x) + (9x)^2)\).
Simplifying further, we get \((5c + 9x)(25c^2 - 45cx + 81x^2)\).
Therefore, \((5c + 9x)(25c^2 - 45cx + 81x^2)\) is the correct factorization of \(125c^3 + 729x^3\).