The expression \( 5a^3 + 2b^3 \) is a sum of cubes. It can be factorized using the sum of cubes formula:

\[
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
\]

For \( 5a^3 + 2b^3 \), we first recognize that the expression doesn’t fit directly into this formula because the coefficients are not 1. Let’s adapt the sum of cubes formula:

\[
5a^3 + 2b^3 = ( \sqrt[3]{5}a + \sqrt[3]{2}b)\left((\sqrt[3]{5}a)^2 - (\sqrt[3]{5}a)(\sqrt[3]{2}b) + (\sqrt[3]{2}b)^2\right)


Learn how to factorize the expression 5a^3 + 2b^3 using the sum of cubes formula. This problem involves algebraic manipulation with polynomials and cubic equations, suitable for advanced high school students.

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