Question

Show that (5x − 3y)2 + 60 xy = (5x + 3y)2

Answer 1

Solution:

We have to show that:

→ (5x - 3y)² + 60xy = (5x + 3y)²

Taking Left Hand Side, we get:

= (5x - 3y)² + 60xy

Using identity (a - b)² = a² - 2ab + b², we get:

= (5x)² - 2 × (5x) × (3y) + (3y)² + 60xy

= 25x² - 30xy + 9y² + 60xy

= 25x² + 30xy + 9y²

Taking Right Hand Side, we get:

= (5x + 3y)²

Using identity (a + b)² = a² + 2ab + b², we get:

= (5x)² + 2 × (5x) × (3y) + (3y)²

= 25x² + 30xy + 9y²

We observe that LHS = RHS

Hence:

→ (5x - 3y)² + 60xy = (5x + 3y)²

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab