Question

Expand (2x + 5y) by identity​

Answer 1

Correct Question

Expand (2x + 5y)^2 and (2x + 5y)^3 by identity

Solution

i) (2x + 5y)²

Applying identity (a+b)² = a² + b² + 2ab

= (2x)² + (5y)² + 2 × 2x × 5y

= 4x² + 25y² + 20xy

ii) (2x + 5y)³

Applying identity (a+b)³ = a³ + b³ + 3ab(a+b)

= (2x)³ + (5y)³ + 3 × 2x × 5y(2x + 5y)

= 8x³ + 125y³ + 30xy(2x + 5y)

= 8x³ + 125y³ + 60x²y + 150xy²

Some important identities

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

Answer 2

CORRECT QUESTION :

( 2x + 5y)² and (2x + 5y)³

Expand by identity

SOLUTION :

( 2x + 5y)²

Identity → (a+b)² = a² + b² +2ab

= (2x)² + (5y)² + 2 × 2x × 5y

= 4x² + 25y² + 20xy

( 2x + 5y)³

Identity → (a+b)³ = a³ + b³ + 3ab(a+b)

= (2x)³ + (5y)³ + 3 × 2x × 5y(2x + 5y)

= 8x³ + 125y³ + 30xy(2x + 5y)

= 8x³ + 125y³ + 60x²y + 150xy²