https://file.aiquickdraw.com/mathbot/file/1726013526428iwimr9hb.jpg

The expression in the image is \( 49x^2 + 56x + 16 \). It seems to be a quadratic expression that likely represents the area of a square or rectangular shape. To find the length of one side, we need to factor this expression and determine the square root of the factored form, assuming it represents a perfect square trinomial.

### Step 1: Check if the trinomial is a perfect square
A perfect square trinomial takes the form:
\[
(a + b)^2 = a^2 + 2ab + b^2
\]
We need to express \( 49x^2 + 56x + 16 \) in this form.

### Step 2: Factor the quadratic expression
\[
49x^2 + 56x + 16 = (7x + 4)^2
\]
This is a perfect square trinomial because:
- \( 7x \) squared gives \( 49x^2 \),
- \( 4 \) squared gives \( 16 \),
- \( 2 \cdot 7x \cdot 4 = 56x \).

### Step 3: Conclusion
Since the quadratic expression factors as \( (7x + 4)^2 \), the length of one side is \( 7x + 4 \).

Let me know if you'd like further details on the factoring process or if you have any other questions!

Here are some related questions:
1. What is a perfect square trinomial?
2. How do you factor quadratic expressions in general?
3. Can a quadratic expression always be factored into perfect squares?
4. How do you solve quadratic equations using factoring?
5. What are other methods to simplify quadratic expressions?

**Tip:** Always verify if a quadratic expression is a perfect square by checking the middle term and the squares of the outer terms!

find the length of one side of the shape represented by the quadratic expression 49x^2 + 56x + 16

Learn how to find the length of one side by factoring the quadratic expression 49x^2 + 56x + 16. This example involves the perfect square trinomial method, making it suitable for students in Grades 9-10. Discover step-by-step solutions to similar problems in algebra.

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