Problem 27 - Algebra 1: Concepts and Skills

Question

Use the distributive property to find the product. $$ (t+8)(t+5) $$

Step-by-Step Solution

Answer

The product of \((t+8)(t+5)\) using the distributive property is \(t^2 + 13t + 40\).

Step 1: Distribute first term of the first binomial

We start by distributing the first term of the first binomial, 't', to both terms of the second binomial. Hence, we have: \(t \cdot t + t \cdot 5\). This simplifies to \(t^2 + 5t\).

Step 2: Distribute second term of the first binomial

Next, distribute the second term of the first binomial, '8', to both terms of the second binomial: \(8 \cdot t + 8 \cdot 5\). This simplifies to \(8t + 40\).

Step 3: Combine Like Terms

Combine the like terms from Step 1 and Step 2: \(t^2 + 5t + 8t + 40\). This simplifies to \(t^2 + 13t + 40\).