Question

formula for solving by differenc3e of squares

Answer 1

The difference of squares identity:

a^2 − b^2 = (a − b)(a + b)

How to use it to solve equations or factor expressions
- Recognize two perfect squares. If you have something of the form A − B where A and B are perfect squares (or can be written as squares), write A = a^2 and B = b^2 and apply the identity.
- To solve A − B = 0 factor it: (a − b)(a + b) = 0, so a − b = 0 or a + b = 0 → a = ±b.

Examples
- x^2 − 9 = (x − 3)(x + 3) → x = ±3.
- 4x^2 − 25 = (2x − 5)(2x + 5) → 2x = ±5 → x = ±5/2.
- 4x^2 − 25y^2 = (2x − 5y)(2x + 5y).

Using substitution where needed
- x^4 − 16 = (x^2)^2 − 4^2 = (x^2 − 4)(x^2 + 4) = (x − 2)(x + 2)(x^2 + 4).
- To solve x^4 − 16 = 0: x = ±2 or x = ±2i (from x^2 + 4 = 0).

Note
- a^2 + b^2 does not factor over the real numbers (except by using complex factors).