Which expression is equivalent to10x2y+25x210x^2y + 25x^210x2y+25x2?

Step 1: Define the Problem

Identify the key components of the expression that need simplification: $10x^2y + 25x^2$.

Step 2: Break Down the Problem

Look for common factors in the terms of the expression:

• The terms are $10x^2y$ and $25x^2$.

Step 3: Apply Relevant Concepts

Factor out the greatest common factor (GCF) from the expression:

• The GCF of $10x^2y$ and $25x^2$ is $5x^2$.

Step 4: Analysis, Verify and Summarize

Factor the expression using the GCF:

• $10x^2y + 25x^2 = 5x^2(2y + 5)$.

Verify by expanding the factored expression:

• $5x^2(2y + 5) = 5x^2 \cdot 2y + 5x^2 \cdot 5 = 10x^2y + 25x^2$.

Final Answer

The expression equivalent to $10x^2y + 25x^2$ is $5x^2(2y + 5)$.