Question

you have a backyard dog pen that is 7 feet long by 5 feet wide. you want more space for your dogs to run around, so you plan to increase the length and width of the pen by x feet.

the total area of the new pen floor can be expressed as \\((x + 7)(x + 5)\\).

to improve your productivity, simplify this expression using distribution.

a.) \\(x^2 + 12x + 35\\)

b.) \\(x^2 + 35x + 12\\)

c.) \\(2x^2 + 12x + 35\\)

Explanation:

Apply the distributive property

$$ (x + 7)(x + 5) = x(x + 5) + 7(x + 5) $$

Expand the terms

$$ x(x + 5) + 7(x + 5) = x^2 + 5x + 7x + 35 $$

Combine like terms

$$ x^2 + (5 + 7)x + 35 = x^2 + 12x + 35 $$

Answer:

• a.) \(x^2 + 12x + 35\) (Correct answer)
• b.) \(x^2 + 35x + 12\)
• c.) \(2x^2 + 12x + 35\)