Which expressions are equivalent to 6x2+36x+54

To find expressions equivalent to \(6x^2 + 36x + 54\), let's factor this quadratic expression.

### Step 1: Factor out the greatest common factor (GCF)
The GCF of \(6x^2\), \(36x\), and \(54\) is 6. We can factor out 6:

\[
6x^2 + 36x + 54 = 6(x^2 + 6x + 9)
\]

### Step 2: Factor the quadratic trinomial inside the parentheses
Now, look at the trinomial \(x^2 + 6x + 9\). This is a perfect square trinomial because:

\[
x^2 + 6x + 9 = (x + 3)^2
\]

### Final factored form:
\[
6x^2 + 36x + 54 = 6(x + 3)^2
\]

Thus, the expression \(6(x + 3)^2\) is equivalent to \(6x^2 + 36x + 54\).

### Equivalent expressions:
- \(6(x^2 + 6x + 9)\)
- \(6(x + 3)^2\)

Both are equivalent to the original expression.

Would you like more details on factoring or have other questions? Here are five related questions:

1. How can you recognize a perfect square trinomial?
2. What is the importance of factoring in simplifying expressions?
3. Can you apply factoring to solve quadratic equations?
4. How would you factor a quadratic expression with no common factor?
5. What are the steps to solving equations using the quadratic formula?

**Tip**: Always check for a common factor first when factoring any polynomial!

Which expressions are equivalent to 6x^2 + 36x + 54?

Explore how to factor the quadratic expression 6x^2 + 36x + 54 by identifying common factors and recognizing perfect square trinomials. This detailed solution guides students through factoring techniques and is ideal for Grades 8-10.

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