Question

FACTORISE
${a}^{2} + \frac{1}{ {a}^{2} } - 2 - 3a + \frac{3}{a}$
make grouping ​

Answer 1

Answer:

a^2+1/a^2-2-3a+3/a

(a-1/a)^2-3(a-1/a)

(a-1/a)(a-1/a-3)

Answer 2

Given :

• a² + 1/a² - 2 - 3a + 3/a

Solution :

Apply identity : (a - b)² = a² + b² - 2ab

→ a² + 1/a² - 2 - 3a + 3/a

→ (a)² + (1/a)² - 2 × a × 1/a - 3a + 3/a

→ (a - 1/a)² - 3a + 3/a

✪ Take 3 as a common ✪

→ (a - 1/a)² - 3(a - 1/a)

✪ Now, take (a - 1/a) as a common ✪

→ (a - 1/a)[(a - 1/a) - 3]

→ (a - 1/a)[a - 1/a - 3]

Some Identities :

• (a + b)² = a² + b² + 2ab
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a² - b² = (a + b)(a - b)
• a³ - b³ = (a - b)(a² + ab + b²)
• a³ + b³ = (a + b)(a² - ab + b²)