Question

Factorize 64a^3+125b^3+240a^b+300ab^​

Answer 1

Correct Question :- Factorize :- 64a^3 + 125b^3 + 240a²b + 300ab² ?

Solution :-

→ 64a^3 + 125b^3 + 240a²b + 300ab²

→ (4a)³ + (5b)³ + 3 * 16a² * 5b + 3 * 4a * 25b²

→ (4a)³ + (5b)³ + 3 * (4a)² * 5b + 3 * 4a * (5b)²

comparing with x³ + y³ + 3x²y + 3xy² = (x + y)³ , we get,

• x = 4a
• y = 5b

Therefore,

→ (4a)³ + (5b)³ + 3 * (4a)² * 5b + 3 * 4a * (5b)²

→ (4a + 5b)³

→ (4a + 5b)(4a + 5b)(4a + 5b)

Hence,

→ 64a^3 + 125b^3 + 240a²b + 300ab² = (4a + 5b)(4a + 5b)(4a + 5b) (Ans.)