To determine which expression is equivalent to [tex]\(10 x^2 y + 25 x^2\)[/tex], let's factor the given polynomial step-by-step.
1. Identify Common Factors:
Both terms [tex]\(10 x^2 y\)[/tex] and [tex]\(25 x^2\)[/tex] share common factors. Specifically, they both contain the factor [tex]\(5 x^2\)[/tex].
- [tex]\(10 x^2 y = 5 x^2 \cdot 2 y\)[/tex]
- [tex]\(25 x^2 = 5 x^2 \cdot 5\)[/tex]
2. Factor out the Common Factor:
Factor [tex]\(5 x^2\)[/tex] out from both terms.
[tex]\[10 x^2 y + 25 x^2 = 5 x^2 (2 y) + 5 x^2 (5)\][/tex]
Combine the terms inside the parenthesis.
[tex]\[10 x^2 y + 25 x^2 = 5 x^2 (2 y + 5)\][/tex]
Thus, the equivalent expression is [tex]\(5 x^2 (2 y + 5)\)[/tex].
Hence, the correct choice is:
[tex]\[ \boxed{5 x^2 (2 y + 5)} \][/tex]
