https://file.aiquickdraw.com/mathbot/file/17303762055885e93idwm.jpg

The expression in the image is as follows:

\[
5 \left( t^2 + \frac{8}{5} t + \left( \frac{4}{5} \right)^2 - \left( \frac{4}{5} \right)^2 + 1 \right)
\]

Let's simplify this step-by-step.

1. **Combine terms inside the parentheses**: Notice that \(\left( \frac{4}{5} \right)^2\) appears twice, once as positive and once as negative, so they cancel each other out. This simplifies to:
   \[
   t^2 + \frac{8}{5} t + 1
   \]

2. **Multiply by 5**: Now we distribute the 5 across each term:
   \[
   5 \times t^2 + 5 \times \frac{8}{5} t + 5 \times 1
   \]

3. **Simplify each term**:
   - \(5 \times t^2 = 5t^2\)
   - \(5 \times \frac{8}{5} t = 8t\)
   - \(5 \times 1 = 5\)

So, the final simplified form of the expression is:

\[
5t^2 + 8t + 5
\]

Would you like more details on the steps or have any questions?

---

Here are five related questions that might help you explore further:

1. How do you factor a quadratic expression like \(5t^2 + 8t + 5\)?
2. Can this expression be solved for \(t\) if it's set equal to zero?
3. How does completing the square work, and can it be applied here?
4. How would you graph the expression \(5t^2 + 8t + 5\)?
5. What are the roots of this quadratic expression if it were an equation?

**Tip**: In quadratic expressions, always check if terms can cancel out to simplify the expression more easily.

Simplify the expression: 5(t^2 + (8/5)t + (4/5)^2 - (4/5)^2 + 1)

Simplify the quadratic expression 5(t^2 + (8/5)t + (4/5)^2 - (4/5)^2 + 1) step-by-step by combining like terms and distributing. Learn essential algebraic simplification techniques for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation