Question

f) p^4 + 2p²q² + q^4​

Answer 1

Answer:

(p² + q²)(p² + q²)  OR  (p² + q²)²

Step-by-step explanation:

• To factorize (p⁴ + 2p²q² + q⁴)

→ p⁴ + 2p²q² + q⁴  ⇒⇒  p⁴ + p²q² + p²q² + q⁴

⇒ p²(p² + q²) + q²(p² + q²)

⇒ (p² + q²)(p² + q²)  ⇔  (p² + q²)²

• To Verify the answer:

Using the identity: a² + b² + 2ab

(p² + q²)² = (p²)² + (q²)² + (2 × p² × q²)

⇒ p⁴ + 2p²q² + q⁴

► HENCE, VERIFIED