Final answer:
Statement 3 should correctly be filled with C) 5b(5+b)-b³, as it appropriately applies the distribution property to the original algebraic expression b(5-b)(5+b) leading to the proof that it equals 25b-b³.
Step-by-step explanation:
The original algebraic expression provided is b(5-b)(5+b) and we're tasked with proving it equals 25b-b³. To complete the proof, we need to correctly fill in Statement 3 using the distribution property.
The correct answer for Statement 3 that completes the proof is C) 5b(5+b)-b³. The reason this is correct is because when we distribute b through the terms (5-b) and (5+b), we effectively use the distribution property twice—first to separate the terms multiplied by b, and then to distribute within the expressions 5b(5+b) and b³(5+b), hence the minus sign between them because we are considering the product of b and -b.
After this step, when we apply the distribution property again in Statement 4, we should expand 5b(5+b) and -b³ independently, which will eventually lead us to the original algebraic expression's equivalent form 25b-b³ after combining like terms.