Final answer:
To simplify the expression (3x + 2)^2 * (2x) * (x + 5)^2 * (2x + 1), we can raise each expression inside the parentheses to the indicated power and then multiply the terms using the distributive property. The simplified expression is 9x^4 + 28x^3 + 49x^2 + 8x.
Step-by-step explanation:
To simplify the expression (3x + 2)^2 * (2x) * (x + 5)^2 * (2x + 1), we can raise each expression inside the parentheses to the power indicated:
(3x + 2)^2 = (3x + 2)(3x + 2) = 9x^2 + 12x + 4
(x + 5)^2 = (x + 5)(x + 5) = x^2 + 10x + 25
Now, we can simplify the entire expression:
(9x^2 + 12x + 4) * (2x) * (x^2 + 10x + 25) * (2x + 1)
Using the distributive property, we can multiply each term:
9x^2 * 2x = 18x^3
12x * 2x = 24x^2
4 * 2x = 8x
x^2 * 9x^2 = 9x^4
x^2 * 10x = 10x^3
x^2 * 25 = 25x^2
Combining like terms, we get:
18x^3 + 24x^2 + 8x + 9x^4 + 10x^3 + 25x^2
Simplifying further:
28x^3 + 49x^2 + 8x + 9x^4
Therefore, the correct option is a) 9x^4 + 28x^3 + 49x^2 + 8x.