The expression given is:

\[ -49 + 4y^2 \]

This expression is a quadratic expression in \( y \).

1. **Standard Form**: The standard form of a quadratic expression is \( ax^2 + bx + c \). In this case, the expression can be rewritten as:

   \[ 4y^2 - 49 \]

2. **Factoring**: The expression is a difference of squares. It can be factored as:

   \[ (2y - 7)(2y + 7) \]

3. **Solutions**: If the expression were set equal to zero, you could solve for \( y \):

   \[ 4y^2 - 49 = 0 \]
   \[ (2y - 7)(2y + 7) = 0 \]

   The solutions would be:

   \[ 2y - 7 = 0 \quad \text{or} \quad 2y + 7 = 0 \]

   So, \( y = \frac{7}{2} \) or \( y = -\frac{7}{2} \).

Let me know if you would like more details or have any questions! Here are some related questions you might find helpful:

1. How do you identify a difference of squares in an expression?
2. Can all quadratic expressions be factored into binomials?
3. What are the steps to complete the square for a quadratic expression?
4. How does the quadratic formula work for solving any quadratic equation?
5. How can you graph a quadratic function, and what does the graph look like?

**Tip:** When factoring quadratic expressions, always check for a difference of squares or a perfect square trinomial, as they can simplify the process.

Learn how to solve the quadratic expression -49 + 4y² with a detailed explanation of factoring and solutions. This problem covers key algebraic concepts, including quadratic equations and difference of squares. Suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation