Algeibraic Identity

3.  IF IN TWO ALGEBRAIC EXPRESSIONS
WHICH CONTAIN LETTERS, FOR ALL
REAL NUMBERS WHICH SETTLE
INSTEAD LETTERS, THEY ARE EQUAL
TO EACH OTHER THEN, THIS
EQUALITY CALLED ALGEBRAIC
IDENTITY.

4.  𝑥 + 𝑦 2 = 𝑥2 + 𝑦2 + 2𝑥𝑦, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 x, y
 Proof
 𝑥 + 𝑦 2 = (𝑥 + 𝑦)(𝑥 + 𝑦)
 = 𝑥 ∗ 𝑥 + 𝑥 ∗ 𝑦 + 𝑦 ∗ 𝑥 + 𝑦 ∗ 𝑦
 = 𝑥2
+ 𝑥𝑦 + 𝑦𝑥 + 𝑦2
 = 𝑥2
+ 𝑥𝑦 + 𝑥𝑦 + 𝑦2
, ( 𝑥𝑦 = 𝑦𝑥)
 = 𝑥2 + 2𝑥𝑦 + 𝑦2

5.  𝑥 − 𝑦 2 = 𝑥2 − 2𝑥𝑦 + 𝑦2, 𝑓𝑜𝑟 𝑎𝑙𝑙 𝑟𝑒𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑥, 𝑦
 Proof
 𝑥 − 𝑦 2 = 𝑥 − 𝑦 𝑥 − 𝑦
 = 𝑥 ∗ 𝑥 − 𝑥 ∗ 𝑦 − 𝑦 ∗ 𝑥 + 𝑦 ∗ 𝑦
 = 𝑥2
− 𝑥𝑦 − 𝑦𝑥 + 𝑦2
 = 𝑥2
− 𝑥𝑦 − 𝑥𝑦 + 𝑦2
, 𝑥𝑦 = 𝑦𝑥
 = 𝑥2 − 2𝑥𝑦 + 𝑦2