Proof of Perfect Square Formula
(i) Proof of (a + b)2
⇒ (a + b)2 = (a + b) × (a + b)
⇒(a + b)2 = a × (a + b) + b × (a + b)
⇒(a + b)2 = a2 + ab + ba + b2
⇒(a + b)2 = a2 + ab + ab + b2 (ba = ab because of commutative law)
⇒(a + b)2 = a2 + 2ab + b2
Hence Proved
(ii) Proof of (a – b)2
⇒(a – b)2 = (a – b) × (a – b)
⇒(a – b)2 = a × (a – b) – b × (a – b)
⇒(a – b)2 = a2 – ab – ba + (-b) × (-b)
⇒(a – b)2 = a2 – ab – ba + b2
⇒(a – b)2 = a2 – ab – ab + b2 (ba=ab because of commutative law)
⇒(a – b)2 = a2 – 2ab + b2
Hence Proved
Perfect Square Formula
Perfect Square Formula: A polynomial or number which when multiplied by itself is called a perfect square. The perfect square is calculated by two algebraic expressions that include: (a + b)² = a² + 2ab + b² and (a – b)² = a² – 2ab + b².
In this article, we have covered the perfect square definition, how to identify perfect square, perfect square formulas, and other related topics in detail.
Table of Content
- What is the Perfect Square Formula?
- How to Identify Perfect Square
- Perfect Square Formula
- Proof of Perfect Square Formula
- Perfect Squares from 1 to 100
- Perfect Square Examples