Question

(6+1​/n)²
expand with the formula ​

Answer 1

Solution:

Given expression:-

$\rm = { \bigg(6 + \dfrac{1}{n} \bigg)}^{2}$

We know that:-

$\rm \longrightarrow {(x + y)}^{2} = {x }^{2} + 2xy + {y}^{2}$

Using this identity, we get:-

$\rm={6}^{2} + \dfrac{1}{ {n}^{2} } + 2 \times 6 \times \dfrac{1}{n}$

$\rm=36 + \dfrac{1}{ {n}^{2} } + \dfrac{12}{n}$

Therefore:-

$\rm \longrightarrow{ \bigg(6 + \dfrac{1}{n} \bigg)}^{2} = 36 + \dfrac{1}{ {n}^{2} } + \dfrac{12}{n}$

★ Which is our required answer.

Learn More:

Algebraic Identities.

• (a - b)² = a² - 2ab + b²
• 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