Question

(x+2y)²-4(x-y)²
please koi bta do​

Answer 1

Solution:

Given to evaluate:

$\tt = {(x + 2y)}^{2} - 4 {(x - y)}^{2}$

Can be written as:

$\tt = {(x + 2y)}^{2} - [2{(x - y)}]^{2}$

$\tt = {(x + 2y)}^{2} - (2x - 2y)^{2}$

Using identity a² - b² = (a + b)(a - b), we get:

$\tt = [(x + 2y) + (2x - 2y)][(x + 2y) - (2x - 2y)]$

$\tt = 3x \times ( - x + 4y)$

$\tt = 3x(4y - x)$

$\tt = 12xy - 3 {x}^{2}$

Which is our required answer.

Answer:

• (x + 2y)² - 4(x - y)² = 12xy - 3x²

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)² + (a - b)² = 2(a² + b²)
• (a + b)² - (a - b)² = 4ab
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac