Answer:
simplified form of (5 + t)(4t + 9) is 4t^2 + 29t + 45.
Explanation:
To expand and simplify the expression (5 + t)(4t + 9), we can use the distributive property. This property states that when we have two terms multiplied together, we can distribute or multiply each term from the first set of parentheses with each term from the second set of parentheses.
Let's break it down step by step:
Step 1: Multiply the first term in the first set of parentheses (5) with each term in the second set of parentheses (4t and 9):
5 * 4t = 20t
5 * 9 = 45
Step 2: Multiply the second term in the first set of parentheses (t) with each term in the second set of parentheses (4t and 9):
t * 4t = 4t^2
t * 9 = 9t
Step 3: Now, we have four terms: 20t, 45, 4t^2, and 9t.
Step 4: Combine like terms, if possible. In this case, we can combine the terms with the same variable:
20t + 9t = 29t
Step 5: Our final expression is: 4t^2 + 29t + 45.