Question

The simplified value of (a²+b²)(a²+b²)- (a²-b²)(a²-b²) is --------.
2a²b²
2a⁴ + 2b⁴ - 2a²b²
4a²b²
none of these​

Answer 1

Answer:

$4 {a}^{2} {b}^{2}$

correct answer

Answer 2

Answer :

The simplified value of (a²+b²)(a²+b²)- (a²-b²)(a²-b²) is 4a²b².

Option c. [ 4a²b² ] is the correct answer.

Step-by-step explanation :

⟹ ( a² + b² ) ( a² + b² ) - ( a² - b² ) ( a² - b² )

⟹ ( a² ) ( a² ) + ( a² ) ( b² ) + ( b² ) ( a² ) + ( b² ) ( b² ) + - a⁴ + 2a²b² + - b⁴

⟹ a⁴ + a²b² + a²b² + b⁴ + - a⁴ + 2a²b² + - b⁴

By combining the like terms

⟹ ( a⁴ - a⁴ ) + ( a²b² + a²b² + 2a²b² ) + ( b⁴ - b⁴ )

Eliminating + a⁴ and - a⁴

⟹ ( a²b² + a²b² + 2a²b² ) + ( b⁴ - b⁴ )

Eliminating + b⁴ - b⁴

⟹a²b² + a²b² + 2a²b²

⟹2a²b² + 2a²b²

⟹ 4a²b²

Hence, the required number is 4a²b².