Question

(a²-b²) (a²+b²) – (a²-b²)²​

Answer 1

Solution :

(a² - b²)( a² + b²) - (a² - b²) ²

> [ a⁴ + a²b² - b²a² - b⁴ ] - [ a⁴ - 2a²b² + b⁴ ]

> [ a⁴ - b⁴ ] - [ a⁴ - 2a²b² + b⁴ ]

> a⁴ - b⁴ - a⁴ + 2a²b² - b⁴

> 2a²b² - b⁴

> b²( 2a² - b²)

This is the required answer.

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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Answer 2

Step-by-step explanation:

Solution :

(a² - b²)( a² + b²) - (a² - b²) ²

> [ a⁴ + a²b² - b²a² - b⁴ ] - [ a⁴ - 2a²b² + b⁴ ]

> [ a⁴ - b⁴ ] - [ a⁴ - 2a²b² + b⁴ ]

> a⁴ - b⁴ - a⁴ + 2a²b² - b⁴

> 2a²b² - b⁴

> b²( 2a² - b²)

This is the required answer.

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Additional Information :

(a + b)² = a² + 2ab + b²

(a + b)² = (a - b)² + 4ab

(a - b)² = a² - 2ab + b²

(a - b)² = (a + b)² - 4ab

a² + b² = (a + b)² - 2ab

a² + b² = (a - b)² + 2ab

2 (a² + b²) = (a + b)² + (a - b)²

4ab = (a + b)² - (a - b)²

ab = {(a + b)/2}² - {(a-b)/2}²

(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

(a + b)³ = a³ + 3a²b + 3ab² b³

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)( a² - ab + b² )

a³ + b³ = (a + b)³ - 3ab( a + b)

a³ - b³ = (a - b)( a² + ab + b²)

a³ - b³ = (a - b)³ + 3ab ( a - b )

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