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The given mathematical expression is:

\[
5x^2 - 6ax - 8a^2
\]

The instruction in Japanese asks to factorize the expression: "を因数分解せよ" translates to "Factor the expression."

Let's proceed with factoring it. The expression \(5x^2 - 6ax - 8a^2\) appears to be a quadratic form in terms of \(x\).

We will look for factors of this quadratic expression.The factored form of the expression \( 5x^2 - 6ax - 8a^2 \) is:

\[
(x - 2a)(5x + 4a)
\]

Would you like a detailed explanation of the factorization process?

Here are 5 related questions for further practice:
1. How do you factorize quadratic expressions?
2. Can all quadratic expressions be factored by simple methods?
3. How do you determine the greatest common factor in expressions like this?
4. How would you handle a similar expression with different coefficients?
5. How do you check if your factorization is correct?

**Tip:** When factorizing quadratic expressions, always check for common factors first to simplify the process.

Learn how to factor the quadratic expression 5x² - 6ax - 8a² step by step. This problem covers key algebraic concepts, including quadratic equations and factorization. Suitable for students in Grades 9-10.

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