We are asked to simplify the expression $x^2(x+2)^2 - 7x(x+2)^2 + 10(x+2)^2$.

1. Problem Description

We are asked to simplify the expression $x^2(x+2)^2 - 7x(x+2)^2 + 10(x+2)^2$.

2. Solution Steps

First, we notice that $(x+2)^2$ is a common factor in all three terms. We can factor it out:

$(x+2)^2(x^2 - 7x + 10)$.

Now we need to factor the quadratic expression $x^2 - 7x + 10$. We are looking for two numbers that multiply to 10 and add to -

7. These numbers are -2 and -

5. Therefore, $x^2 - 7x + 10 = (x - 2)(x - 5)$.

So, the original expression becomes $(x+2)^2(x-2)(x-5)$.

3. Final Answer

$(x+2)^2(x-2)(x-5)$