Verify the Expansion: Is (a+b)(c+d) = ab+cd+ac+bd Correct?

To determine if the given equality $(a+b)(c+d) = ab + cd + ac + bd$ is correct, let's expand $(a+b)(c+d)$ using the distributive property:

Step 1: Use the distributive property to expand $(a+b)(c+d)$. We distribute each term in the first parenthesis by each term in the second parenthesis:

• $a(c+d) = ac + ad$
• $b(c+d) = bc + bd$

Step 2: Combine all the terms obtained from the distributive process:

$ac + ad + bc + bd$

Step 3: Compare the expanded form $ac + ad + bc + bd$ with the right-hand side of the given equality $ab + cd + ac + bd$:

The terms do not match, as the expanded form has terms $ad$ and $bc$ instead of $ab$ and $cd$.

Therefore, the correct expanded form is $ac + ad + bc + bd$. Hence, the given equality is not correct.

The correct answer is: No, it must be $ac + ad + bc + bd$.