Distributive Property: Simplifying (a+c+d)(a+e) Step-by-Step

To solve this problem using the distributive property, let's expand the given expression $(a+c+d)(a+e)$ step by step.

Step 1: Expand $(a+c+d)(a+e)$ using the distributive property:

• Distribute $a$ over $(a+e)$:
  $a(a+e) = a^2 + ae$
• Distribute $c$ over $(a+e)$:
  $c(a+e) = ca + ce$
• Distribute $d$ over $(a+e)$:
  $d(a+e) = da + de$

Step 2: Combine all distributed terms:

$a^2 + ae + ca + ce + da + de$

Thus, the expression simplifies to $\bm{a^2 + ae + ca + ce + da + de}$.

Therefore, the solution to the problem is Yes, $(a^2 + ae + ca + ce + da + de)$, which matches choice 3.