Question

Solve this please and give answer ASAP.
This is a question on algebraic identities.
$(x + y)^{2} + 2(x + y)(x - y) + (x - y) ^{2}$
No spamming or inappropriate answers ​

Answer 1

Topic :-

Algebraic Identities

To Simplify:-

(x + y)² + 2(x + y)(x - y) + (x - y)²

Solution :-

→ (x + y)² + 2(x + y)(x - y) + (x - y)²

→ x² + 2xy + y² + 2(x + y)(x - y) + (x - y)²

( ∵ (a + b)² = a² + 2ab + b² )

→ x² + 2xy + y² + 2(x² - y²) + (x - y)²

( ∵ (a + b)(a - b) = a² - b² )

→ x² + 2xy + y² + 2x² - 2y² + (x - y)²

→ (x² + 2x²) + (y² - 2y²) + 2xy + (x - y)²

→ 3x² - y² + 2xy + (x - y)²

→ 3x² - y² + 2xy + x² - 2xy + y²

( ∵ (a- b)² = a² - 2ab + b²)

→ (3x² + x²) + (y² - y²) + (2xy - 2xy)

→ 4x² + 0 + 0

→ 4x²

Answer :-

(x + y)² + 2(x + y)(x - y) + (x - y)² = 4x²

Additional Formulae :-

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

a⁴ + a² + 1 = (a² + 1 + a)(a² + 1 - a)