(x+7)(x-7)=0quadratic equation in standard form, then identify the values of a, b, and c.

The given equation is \((x + 7)(x - 7) = 0\). To write it in the standard form of a quadratic equation, which is \(ax^2 + bx + c = 0\), we first need to expand the given expression.

1. Expand the product:
\[
(x + 7)(x - 7) = x^2 - 7x + 7x - 49
\]

2. Simplify the expression:
\[
x^2 - 49 = 0
\]

This is the quadratic equation in its expanded form.

To match it to the standard form \(ax^2 + bx + c = 0\):
\[
x^2 + 0x - 49 = 0
\]

Here:
- \(a = 1\) (coefficient of \(x^2\))
- \(b = 0\) (coefficient of \(x\))
- \(c = -49\) (constant term)

### Summary:
- The quadratic equation in standard form: \(x^2 + 0x - 49 = 0\)
- Values:
  - \(a = 1\)
  - \(b = 0\)
  - \(c = -49\)

Would you like further details or have any questions?

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Here are 8 related questions you might find useful:
1. How do you solve the equation \(x^2 - 49 = 0\)?
2. What is the vertex form of a quadratic equation?
3. How do you find the roots of the equation \(x^2 - 49 = 0\)?
4. What are the properties of the quadratic equation \(x^2 + 0x - 49 = 0\)?
5. How does the discriminant of a quadratic equation help in determining the nature of its roots?
6. What is the axis of symmetry for the equation \(x^2 + 0x - 49 = 0\)?
7. How do you graph the quadratic equation \(x^2 - 49 = 0\)?
8. How would the values of \(a\), \(b\), and \(c\) change if the equation was \(2x^2 - 49 = 0\)?

**Tip:** The discriminant \(\Delta\) of a quadratic equation \(ax^2 + bx + c = 0\) is given by \(b^2 - 4ac\). It helps determine the nature of the roots: real and distinct, real and equal, or complex.

Explore how to solve the quadratic equation (x + 7)(x - 7) = 0 step-by-step. Learn about expanding binomials, identifying coefficients in quadratic equations, and understanding the standard form of quadratic equations. Suitable for high school students.

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