Verify the Expansion: (a+4)(x+b+c)=ax+ab+ac+4

Is equality correct?

$(a+4)(x+b+c)=ax+ab+ac+4$

To address the question about the equality, we will simplify both sides of the given expression:

The left-hand side of the expression is $(a+4)(x+b+c)$.

• Applying the distributive property, expand $(a+4)$ over $(x+b+c)$:

$(a+4)(x+b+c) = a(x+b+c) + 4(x+b+c)$.

Next, further distribute $a$ and $4$ over each term inside the parentheses:

$a(x+b+c) = ax + ab + ac$
$4(x+b+c) = 4x + 4b + 4c$.

So, the expanded form becomes:

$ax + ab + ac + 4x + 4b + 4c$.

Comparing this with the right-hand side, which is $ax + ab + ac + 4$, observe that:

• Both sides have the terms $ax + ab + ac$.
• However, the left-hand side has additional terms $4x + 4b + 4c$ which the right-hand side does not include.
• The constant term $4$ on the right-hand side does not match these additional terms.

Thus, the equality $(a+4)(x+b+c) = ax + ab + ac + 4$ is not correct.

Therefore, the expression is only right if stated differently. Reviewing the choices:

• Choice 2 correctly presents the restructured expression that would validate the equality: $(x+b+c)a+4$.

Hence, the correct response is choice 2: No, it would be true if the expression were $(x+b+c)a+4$.