ALGEBRA IDENTITIES

(x + y)² (and what is the #1 Trap?)

x² + 2xy + y²

Simplify (x - y)² (how does it differ from the Plus version?)

x² - 2xy + y²

only difference is the negative sign on the middle term.

Simplify (x + y)(x - y)

x² - y²

Use this whenever you see a subtraction of two squared numbers.

If I see x² + 6x + 9, what identity is hiding here?

This expression is a perfect square trinomial and can be factored as (x + 3)²

Simplify: (100² - 99²) / 199

Step 1 (Structure): Look at the top (100² - 99²). It is a subtraction of two squares.

Step 2 (Rewrite): Use Identity 3 to change the top to: (100 + 99)(100 - 99).

Step 3 (Solve): * (100 + 99) = 199

• (100 - 99) = 1

• So the top is 199 * 1.

Final Result: 199 / 199 = 1.

(x-1)(x+1)

x² - 1.

A whole number x can always be rewritten as square x square to cancel terms in a fraction.

square root as "half" of a number's power. When you multiply two "halves" together, you get the "whole”

A "Square Root" is literally half of a multiplication.