https://file.aiquickdraw.com/mathbot/file/1726179195306h1lpx710.jpg

The expression shown in the image is:

\[
25x^2 + 90x + 81
\]

We are asked to factor it. This is a quadratic trinomial. Let's attempt to factor it.

### Step 1: Check if it is a perfect square trinomial

A perfect square trinomial takes the form \((ax + b)^2 = a^2x^2 + 2abx + b^2\).

- \(25x^2\) is a perfect square, as \((5x)^2 = 25x^2\).
- \(81\) is also a perfect square, as \(9^2 = 81\).
- The middle term is \(90x\), and we can check if it equals \(2 \times 5x \times 9\), which is \(90x\). It does.

### Step 2: Write the factorization

Since the expression is a perfect square trinomial, we can write it as:

\[
(5x + 9)^2
\]

Thus, the factorization of \(25x^2 + 90x + 81\) is:

\[
(5x + 9)(5x + 9) \quad \text{or} \quad (5x + 9)^2
\]

Would you like more details on this factorization process or do you have any further questions?

### Related Questions:

1. How do you recognize a perfect square trinomial?
2. Can all quadratic expressions be factored as perfect squares?
3. How can the quadratic formula be used if a trinomial is not factorable?
4. What are other methods of factoring trinomials?
5. How would you expand \((5x + 9)^2\) back to its original form?

**Tip**: Always check for the greatest common factor (GCF) before factoring any quadratic expression to simplify the process.

Learn how to factor the perfect square trinomial 25x^2 + 90x + 81 step-by-step. This guide explains the algebraic process and provides insight into recognizing perfect square trinomials, suitable for Grades 9-10 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation