Questions: The expression (4 t-3)(4 t+5)+2 t-5 equals A t^2+B t+C where A equals: and B equals: and C equals:

Solution Steps

To solve the given expression \((4t-3)(4t+5) + 2t - 5\) and express it in the form \(At^2 + Bt + C\), we need to:

1. Expand the product \((4t-3)(4t+5)\) using the distributive property (FOIL method).
2. Combine like terms from the expanded expression and the remaining terms \(2t - 5\).
3. Identify the coefficients \(A\), \(B\), and \(C\) from the resulting polynomial.

We start with the expression \((4t - 3)(4t + 5) + 2t - 5\). First, we expand the product using the distributive property:

\[ (4t - 3)(4t + 5) = 4t \cdot 4t + 4t \cdot 5 - 3 \cdot 4t - 3 \cdot 5 = 16t^2 + 20t - 12t - 15 \]

This simplifies to:

\[ 16t^2 + 8t - 15 \]

Next, we add the remaining terms \(2t - 5\) to the expanded expression:

\[ 16t^2 + 8t - 15 + 2t - 5 = 16t^2 + (8t + 2t) + (-15 - 5) = 16t^2 + 10t - 20 \]

From the final expression \(16t^2 + 10t - 20\), we can identify the coefficients:

• \(A = 16\)
• \(B = 10\)
• \(C = -20\)

Final Answer