Question

Which of the following is the simplified polynomial that represents the area of a square with a side length of (a+b + ab)?

A. a^3b^2 + a^2b^2
B. 2a^4b^2 + 2a^2b^2
C. a'b^2 + 2a^2b^2 + ab
D. a^4b^2 + 2a^3b^2 + a^2b^2

Answer 1

Option C). The simplified polynomial that represents the area of a square with a side length of (a+b + ab) is a^2 + b^2 + 2ab + a^2b^2 + 2ab^2 + 2a^2b.

Step-by-step explanation:

The area of a square is found by multiplying the length of one of its sides by itself. In this case, the side length is (a+b+ab). So, the simplified polynomial that represents the area of the square is:

(a+b+ab) * (a+b+ab) = (a+b+ab)^2

Expanding this using the distributive property, we get:

(a+b+ab)^2 = (a+b+ab) * (a+b+ab) = a^2 + ab + ba + b^2 + ab + ba + a^2b^2 + 2ab^2 + 2a^2b

Combining like terms, we can further simplify it to:

a^2 + b^2 + 2ab + a^2b^2 + 2ab^2 + 2a^2b

Therefore, the correct answer is option C: a^2 + b^2 + 2ab + a^2b^2 + 2ab^2 + 2a^2b.