Question

simplify
(a^2+b^2)^2 - (a^2-b^2)^2​

Answer 1

Step-by-step explanation:

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Answer 2

$\blue\bigstar$Answer:

• (a² + b²)² - (a² - b²)² = 4a²b²

$\pink\bigstar$ Given:

• (a² + b²)² - (a² - b²)²

$\green\bigstar$To find:

• To Simplify : (a² + b²)² - (a² - b²)²

$\blue\bigstar$ Solution:

(a² + b²)² - (a² - b²)²

$\implies$(a² + b²)² - {(a - b)(a + b)}²

[ By using (a + b)(a - b) = a² - b² ]

$\implies$ (a² + b²)² - {(a - b)(a + b)}²

$\implies$(a² + b²)² - {(a - b)²}{(a + b)²}

[ By using {(a)(b)}² = a²b² ]

$\implies$(a² + b²)² - {a² - 2ab + b²}{a² + 2ab + b²}

[ By using (a + b)² = a² + 2ab + b² and (a - b)² = a² - 2ab + b² ]

$\implies$(a⁴ + 2a²b² + b⁴) - {a² - 2ab + b²}{a² + 2ab + b²}

[ By using (a + b)² = a² + b² + 2ab ]

$\implies$ (a⁴ + 2a²b² + b⁴) - { a⁴ + 2a³b + a²b² - 2a³b - 4a²b² - 2ab³ + a²b² + 2ab³ + b⁴ }

$\implies$(a⁴ + 2a²b² + b⁴) - (a⁴ + a²b² - 4a²b² + a²b² + b⁴)

$\implies$(a⁴ + 2a²b² + b⁴) - (a⁴ + 2a²b² - 4a²b² + b⁴)

$\implies$(a⁴ + 2a²b² + b⁴) - (a⁴ - 2a²b² + b⁴)

$\implies$a⁴ + 2a²b² + b⁴ - a⁴ + 2a²b² - b⁴

$\implies$4a²b²

$\therefore$ (a² + b²)² - (a² - b²)² = 4a²b²

$\pink\bigstar$ Concepts Used:

• (a + b)(a - b) = a² - b²
• {(a)(b)}² = a²b²
• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• Negative × Negative = Positive

$\red\bigstar$Extra - Information:

• (x + a)(x + b) = x² + (a + b) x + ab

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

• (a + b)³ = a³ + b³ + 3ab (a + b)

• (a – b)³ = a³ – b³ – 3ab (a – b)

• a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² – ab – bc – ca)

• a³ + b³ = (a + b)(a² - ab + b²)