1. **State the problem:** Factorize the expression $$8x^4 - 26x^2m^2 + 18m^4$$. 2. **Identify the type of expression:** This is a quadratic form in terms of $x^2$ and $m^2$. 3. **Rewrite the expression:** Let $a = x^2$ and $b = m^2$, then the expression becomes $$8a^2 - 26ab + 18b^2$$. 4. **Use the quadratic factoring method:** We look for two numbers that multiply to $$8 \times 18 = 144$$ and add to $$-26$$. 5. **Find the pair:** The numbers are $$-18$$ and $$-8$$ because $$-18 \times -8 = 144$$ and $$-18 + (-8) = -26$$. 6. **Rewrite the middle term:** $$8a^2 - 18ab - 8ab + 18b^2$$. 7. **Group terms:** $$(8a^2 - 18ab) + (-8ab + 18b^2)$$. 8. **Factor each group:** $$2a(4a - 9b) - 2b(4a - 9b)$$. 9. **Factor out the common binomial:** $$(2a - 2b)(4a - 9b)$$. 10. **Substitute back:** $$(2x^2 - 2m^2)(4x^2 - 9m^2)$$. 11. **Factor further if possible:** Note that $$2x^2 - 2m^2 = 2(x^2 - m^2)$$ and $$4x^2 - 9m^2$$ is a difference of squares. 12. **Apply difference of squares:** $$x^2 - m^2 = (x - m)(x + m)$$ and $$4x^2 - 9m^2 = (2x - 3m)(2x + 3m)$$. 13. **Final factorization:** $$2(x - m)(x + m)(2x - 3m)(2x + 3m)$$. **Answer:** The factorized form is $$2(x - m)(x + m)(2x - 3m)(2x + 3m)$$.