https://file.aiquickdraw.com/mathbot/file/1726452209948zws8zuxb.jpg

The expression given in the image is:

\[
25x^2 - 20x + 4
\]

To factor this trinomial, we'll look for a pair of binomials that multiply together to give the original expression.

### Step 1: Check for a common factor
There is no common factor that divides all the terms of the trinomial.

### Step 2: Apply factoring by grouping or use a factoring method

The expression appears to be a quadratic in the form \( ax^2 + bx + c \), where:

- \( a = 25 \)
- \( b = -20 \)
- \( c = 4 \)

### Step 3: Factor using trial or the AC method
Multiply \( a \times c = 25 \times 4 = 100 \).

We need two numbers that multiply to 100 and add to \( b = -20 \). These numbers are \( -10 \) and \( -10 \), because:

\[
-10 \times -10 = 100
\quad \text{and} \quad -10 + -10 = -20
\]

Thus, we can rewrite the middle term as:

\[
25x^2 - 10x - 10x + 4
\]

### Step 4: Factor by grouping
Group the terms:

\[
(25x^2 - 10x) - (10x - 4)
\]

Factor out the greatest common factor (GCF) from each group:

\[
5x(5x - 2) - 2(5x - 2)
\]

Now, factor out the common binomial factor:

\[
(5x - 2)(5x - 2)
\]

### Final Factored Form:
\[
(5x - 2)^2
\]

Thus, the factored form of \( 25x^2 - 20x + 4 \) is:

\[
(5x - 2)^2
\]

Would you like further details or explanations on any of the steps?

Here are 5 related questions for you:
1. How do you factor trinomials where the leading coefficient is greater than 1?
2. What is the AC method for factoring trinomials?
3. Can all quadratic trinomials be factored into binomials?
4. How can factoring help solve quadratic equations?
5. What is the difference between factoring and expanding polynomials?

**Tip**: Always check for a greatest common factor (GCF) first before proceeding to more complex factoring methods.

Learn how to factor the trinomial 25x^2 - 20x + 4 using the AC method and grouping. Follow a step-by-step guide to rewrite the expression and factor it completely. Suitable for students in Grades 9-11.

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